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Friday, 10 August 2012

Angie Donohue recently opened her own basketweaving studio. She sells finished baskets in addition

Angie Donohue recently opened her own basketweaving studio. She sells finished baskets in addition to the raw materials needed by customers to weave baskets of their own. Angie has put together a variety of raw material kits, each including materials at various stages of completion. Unfortunately, owing to space limitations, Angie is unable to carry all varieties of kits originally assembled and must choose between two basic packages.

The basic introductory kit includes undyed, uncut reeds (with dye included) for weaving one basket. This basic package costs Angie $11.70 and sells for $26.55. The second kit, called Stage 2, includes cut reeds that have already been dyed. With this kit the customer need only soak the reeds and weave the basket. Angie is able to produce the second kit by using the basic materials included in the first kit and adding one hour of her own time (to produce two kits), which she values at $17.60 per hour. Because she is more efficient at cutting and dying reeds than her average customer, Angie is able to make two kits of the dyed reeds, in one hour, from one kit of undyed reeds. The kit of dyed and cut reeds sells for $34.64.

Determine whether Angie’s basketweaving shop should carry the basic introductory kit with undyed and uncut reeds, or the Stage 2 kit with reeds already dyed and cut. Prepare an incremental analysis to support your answer. (Round answers to 2 decimal places, e.g. $2.45. If an amount reduces the net income for Increase (Decrease) column then enter with a negative sign preceding the number e.g. -15,000 or parenthesis, e.g. (15,000). Enter all other amounts in all other columns as positive and subtract where necessary.)

	Sell (Basic Kit)	Process Further (Stage 2 Kit)	Net Income Increase (Decrease)
Sales per unit	$	$	$
Costs per unit
	$	$	$

Total	$	$	$
Net income/(loss) per unit	$	$	$

Angie’s basketweaving shop should carry the .

Taylor Corp. is growing quickly. Dividends are expected to grow at a 28 percent rate for the next

Taylor Corp. is growing quickly. Dividends are expected to grow at a 28 percent rate for the next three years, with the growth rate falling off to a constant 7.9 percent thereafter.

Required:

If the required return is 16 percent and the company just paid a $3.70 dividend, what is the current share price? (Hint: Calculate the first four dividends.) (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Current share price

Explanation:

With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as:

P₃ = D₃ (1 + g₂) / (R – g₂)

P₃ = D₀ (1 + g₁)³ (1 + g₂) / (R – g₂)

P₃ = $3.70(1.28)³(1.079) / (0.16 – 0.079)

P₃ = $103.36

The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be:

P₀ = $3.70(1.28) / 1.16 + $3.70(1.28)²/ 1.16² + $3.70(1.28)³/ 1.16³ + $103.36 / 1.16³

P₀ = $79.78

Apocalyptica Corporation is expected to pay the following dividends over the next four years:

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $5.60, $16.60, $21.60, and $3.40. Afterwards, the company pledges to maintain a constant 5.25 percent growth rate in dividends, forever.

Required:

If the required return on the stock is 9 percent, what is the current share price? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Current share price

Explanation:

With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as:

P₄ = D₄ (1 + g) / (R – g)

P₄ = $3.40(1.0525) / (0.09 – 0.0525)

P₄ = $95.43

The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be:

P₀ = $5.60 / 1.09 + $16.60 / 1.09² + $21.60 / 1.09³ + $3.40 / 1.09⁴ + $95.43 / 1.09⁴

P₀ = $105.80

The stock price of Jenkins Co. is $54.70. Investors require a 13 percent rate of return on similar stocks.

Required:

If the company plans to pay a dividend of $4.00 next year, what growth rate is expected for the company’s stock price? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

Growth rate

Explanation:

We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g. Doing so, we find:

g = R – (D₁ / P₀)

g = 0.13 – ($4.00 / $54.70)

g = 0.0569 or 5.69%

Gesto, Inc., has an issue of preferred stock outstanding that pays a $4.90 dividend every year, in perpetuity.

Required:

If this issue currently sells for $80.05 per share, what is the required return? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

Required return

Explanation:

The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. This is a special case of the dividend growth model where the growth rate is zero, or the level perpetuity equation. Using this equation, we find the price per share of the preferred stock is:

R = D/P₀

R = $4.90/$80.05

R = 0.0612 or 6.12%

Ziggs Corporation will pay a $4.20 per share dividend next year.

Ziggs Corporation will pay a $4.20 per share dividend next year. The company pledges to increase its dividend by 6.50 percent per year, indefinitely.

Required:

If you require a 10 percent return on your investment, how much will you pay for the company’s stock today? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Current stock price

Explanation:

Using the constant growth model, we find the price of the stock today is:

P₀ = D₁ / (R – g)

P₀ = $4.20 / (0.10 – 0.0650)

P₀ = $120.00

The next dividend payment by Mosby, Inc., will be $2.85 per share. The dividends are anticipated to

The next dividend payment by Mosby, Inc., will be $2.85 per share. The dividends are anticipated to maintain a 7.50 percent growth rate, forever. Assume the stock currently sells for $49.30 per share.

Requirement 1:

What is the dividend yield? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

Dividend yield

Requirement 2:

What is the expected capital gains yield? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

Capital gains yield

Explanation: 1:

The dividend yield is the dividend next year divided by the current price, so the dividend yield is:

Dividend yield = D₁ / P₀

Dividend yield = $2.85 / $49.30

Dividend yield = 0.0578 or 5.78%

The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:

Capital gains yield = 7.50%

The next dividend payment by Mosby, Inc., will be $3.30 per share. The dividends are anticipated to

The next dividend payment by Mosby, Inc., will be $3.30 per share. The dividends are anticipated to maintain a 2.75 percent growth rate, forever.

Required:

If the stock currently sells for $50.20 per share, what is the required return? (Do not include the percent sign (%). Round your answer to 2 decimal places (e.g., 32.16).)

Required return

Explanation:

We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find:

R = (D₁ / P₀) + g

R = ($3.30 / $50.20) + 0.0275

R = 0.0932 or 9.32%

Patience, Inc., just paid a dividend of $2.80 per share on its stock. The dividends are expected to

Patience, Inc., just paid a dividend of $2.80 per share on its stock. The dividends are expected to grow at a constant rate of 6.75 percent per year, indefinitely. Assume investors require an 12 percent return on this stock.

Requirement 1:

What is the current price? (Do not include the dollar sign ($). Round your answer to 2 decimal places (e.g., 32.16).)

Current price

Requirement 2:

What will the price be in four years and in sixteen years? (Do not include the dollar signs ($). Round your answers to 2 decimal places (e.g., 32.16).)


Four years	$
Sixteen years	$

Explanation: 1:

The constant dividend growth model is:

P_t = D_t × (1 + g) / (R – g)

So, the price of the stock today is:

P₀ = D₀ (1 + g) / (R – g)

P₀ = $2.80 (1.0675) / (0.12 – 0.0675)

P₀ = $56.93

The dividend at year 5 is the dividend today times the FVIF for the growth rate in dividends and five years, so:

P₄ = D₄ (1 + g) / (R – g)

P₄ = D₀ (1 + g)⁵ / (R – g)

P₄ = $2.80 (1.0675)⁵ / (0.12 – 0.0675)

P₄ = $73.93

We can do the same thing to find the dividend in Year 17, which gives us the price in Year 16, so:

P₁₆ = D₁₆ (1 + g) / (R – g)

P₁₆ = D₀ (1 + g)¹⁷ / (R – g)

P₁₆ = $2.80 (1.0675)¹⁷ / (0.12 – 0.0675)

P₁₆ = $161.90

There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in four years, and we have already calculated the stock price today. The stock price in four years will be:

P₄ = P₀(1 + g)⁴

P₄ = $56.93(1 + 0.0675)⁴

P₄ = $73.93

And the stock price in 16 years will be:

P₁₆ = P₀(1 + g)¹⁶

P₁₆ = $56.93(1 + 0.0675)¹⁶

P₁₆ = $161.90

An investment offers a 11 percent total return over the coming year. Bill Bernanke thinks the total real return on this investment will be only 8.4 percent.

Required:

What does Bill believe the inflation rate will be over the next year? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Inflation rate

Explanation:

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

h = [(1 + 0.11) / (1 + 0.084)] – 1

h = 0.0240 or 2.40%

Suppose the real rate is 3.40 percent and the inflation rate is 2.2 percent.

Required:

What rate would you expect to see on a Treasury bill? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Rate

Explanation:

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation, is:

(1 + R) = (1 + r)(1 + h)

R = (1 + 0.0340)(1 + 0.022) – 1

R = 0.0567 or 5.67%

App Store Co. issued 15-year bonds one year ago at a coupon rate of 7.6 percent. The bonds make semiannual payments.

Required:

If the YTM on these bonds is 5.3 percent, what is the current bond price? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current bond price

rev: 05-02-2011

Explanation:

To find the price of this bond, we need to realize that the maturity of the bond is 14 years. The bond was issued one year ago, with 15 years to maturity, so there are 14 years left on the bond. Also, the coupons are semiannual, so we need to use the semiannual interest rate and the number of semiannual periods. The price of the bond is:

P = $38.00(PVIFA_2.65%,28) + $1,000(PVIF_2.65%,28)

P = $1,225.32

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

14 × 2

5.3% / 2

±$76 / 2

±$1,000

I/Y

PMT

Solve for

$1,225.32

Merton Enterprises has bonds on the market making annual payments, with 15 years to maturity, and selling for $971. At this price, the bonds yield 8.3 percent.

Required:

What must the coupon rate be on Merton’s bonds? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16). )

Coupon rate

rev: 05-02-2011

Explanation:

Here we need to find the coupon rate of the bond. All we need to do is to set up the bond pricing equation and solve for the coupon payment as follows:

P = $971 = C(PVIFA_8.3%,15) + $1,000(PVIF_8.3%,15)

Solving for the coupon payment, we get:

C = $79.55

The coupon payment is the coupon rate times par value. Using this relationship, we get:

Coupon rate = $79.55 / $1,000

Coupon rate = 0.0795 or 7.95%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

8.3%

±$971

$1,000

I/Y

PMT

Solve for

$79.55

Coupon rate = $79.55 / $1,000

Coupon rate = 0.0795 or 7.95%

The Timberlake-Jackson Wardrobe Co. has 11.4 percent coupon bonds on the market with seven years left to maturity. The bonds make annual payments.

Required:

If the bond currently sells for $1,115.37, what is its YTM? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Yield to maturity

rev: 05-02-2011

Explanation:

Here, we need to find the YTM of a bond. The equation for the bond price is:

P = $1,115.37 = $114(PVIFA_R%_,7) + $1,000(PVIF_R_%,7)

Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find:

R = YTM = 9.10%

If you are using trial and error to find the YTM of the bond, you might be wondering how to pick an interest rate to start the process. First, we know the YTM has to be lower than the coupon rate since the bond is a premium bond. That still leaves a lot of interest rates to check. One way to get a starting point is to use the following equation, which will give you an approximation of the YTM:

Approximate YTM = [Annual interest payment + (Par value – Price) / Years to maturity] / [(Price + Par value) / 2]

Solving for this problem, we get:

Approximate YTM = [$114 + (–$115.37 / 7)] / [($1,115.37 + 1,000) / 2]

Approximate YTM = .0922 or 9.22%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

±$1,115.37

$114

$1,000

I/Y

PMT

Solve for

9.10%

Lycan, Inc., has 8.6 percent coupon bonds on the market that have 9 years left to maturity. The bonds make annual payments.

Required:

If the YTM on these bonds is 10.6 percent, what is the current bond price? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current bond price

rev: 05-02-2011

Explanation:

The price of any bond is the PV of the interest payments, plus the PV of the par value. Notice this problem assumes an annual coupon. The price of the bond will be:

P = $86({1 – [1/(1 + 0.106)]⁹} / 0.106) + $1,000[1 / (1 + 0.106)⁹]

P = $887.52

We would like to introduce shorthand notation here. Rather than write (or type, as the case may be) the entire equation for the PV of a lump sum, or the PVA equation, it is common to abbreviate the equations as:

PVIF_R,t = 1 / (1 + R)^t

which stands for Present Value Interest Factor

PVIFA_R,t = ({1 – [1/(1 + R)]^t } / R)

which stands for Present Value Interest Factor of an Annuity

These abbreviations are shorthand notation for the equations in which the interest rate and the number of periods are substituted into the equation and solved. We will use this shorthand notation in the remainder of the solutions key. The bond price equation for this problem would be:

P = $86(PVIFA_10.6%,9) + $1,000(PVIF_10.6_%,₉)

P = $887.52

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

10.6%

±$86

±$1,000

I/Y

PMT

Solve for

$887.52

You have arranged for a loan on your new car that will require the first payment today. The loan is for $43,500, and the monthly payments are $740.

Required:

If the loan will be paid off over the next 79 months, what is the APR of the loan? (Do not include the percent sign (%). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

APR

rev: 05-02-2011

Explanation:

Here we are given the PVA for an annuity due, number of periods, and the amount of the annuity. We need to solve for the interest rate. Using the PVA equation:

PVA = [{1 – [1 / (1 + r)]⁷⁹}/ r](1 + r)

$43,500 = $740[{1 – [1 / (1 + r)]⁷⁹}/ r](1 + r)

To find the interest rate, we need to solve this equation on a financial calculator, using a spreadsheet, or by trial and error. If you use trial and error, remember that increasing the interest rate decreases the PVA, and decreasing the interest rate increases the PVA. Using a spreadsheet, we find:

r = 0.0080 or 0.80%

This is the monthly interest rate. To find the APR with a monthly interest rate, we simply multiply the monthly rate by 12, so the APR is:

APR = 0.0080 × 12

APR = 0.0964 or 9.64%

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

2^nd BGN 2^nd SET

Enter

±$43,500

$740

I/Y

PMT

Solve for

0.80%

APR = 0.80%(12) = 9.64%

One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a

One of your customers is delinquent on his accounts payable balance. You’ve mutually agreed to a repayment schedule of $560 per month. You will charge 0.96 percent per month interest on the overdue balance.

Required:

If the current balance is $14,780, how long will it take for the account to be paid off? (Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Number of months

rev: 04-30-2011

Explanation:

Here we need to find the length of an annuity. We know the interest rate, the PV, and the payments. Using the PVA equation:

PVA = C({1 – [1/(1 + r)^t]} / r )

$14,780 = $560{ [1 – (1/1.0096)^t ] / 0.0096}

Now we solve for t:

1/1.0096^t = 1 – [($14,780)(0.0096) / ($560)]

1.0096^t = 1 / 0.74663 = 1.33935

t = ln 1.33935 / ln 1.0096

t = 30.58 months

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

0.96%

$14,780

±$560

I/Y

PMT

Solve for

30.58

Bucher Credit Bank is offering 5.9 percent compounded daily on its savings accounts. Assume that you deposit $5,600 today.

Requirement 1:

How much will you have in the account in 4 years? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Use 365 days in a year. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

Requirement 2:

How much will you have in the account in 8 years? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Use 365 days in a year. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

Requirement 3:

How much will you have in the account in 16 years? (Do not include the dollar sign ($). Enter rounded answer as directed, but do not use the rounded numbers in intermediate calculations. Use 365 days in a year. Round your answer to 2 decimal places (e.g., 32.16).)

Future value

rev: 04-30-2011

Explanation:

For this problem, we simply need to find the FV of a lump sum using the equation:

FV = PV(1 + r)^t

It is important to note that compounding occurs daily. To account for this, we will divide the interest rate by 365 (the number of days in a year, ignoring leap year), and multiply the number of periods by 365. Doing so, we get:

FV in 4 years	= $5,600[1 + (0.059/365)]⁴⁽³⁶⁵⁾	= $7,090.44
FV in 8 years	= $5,600[1 + (0.059/365)]⁸⁽³⁶⁵⁾	= $8,977.56
FV in 16 years	= $5,600[1 + (0.059/365)]^16(365)	= $14,392.26

Calculator Solution:

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Enter

4 × 365

5.9% / 365

±$5,600

I/Y

PMT

Solve for

$7,090.44

Enter

8 × 365

5.9% / 365

±$5,600

I/Y

PMT

Solve for

$8,977.56

Enter

16 × 365

5.9% / 365

±$5,600

I/Y

PMT

Solve for

$14,392.26

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Friday, 10 August 2012