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.

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(PVIFA8.3%,15) + $1,000(PVIF8.3%,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

15

8.3%

±$971

$1,000

N

I/Y

PV

PMT

FV

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.

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(PVIFAR%,7) + $1,000(PVIFR%,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

7

±$1,115.37

$114

$1,000

N

I/Y

PV

PMT

FV

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.

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:

PVIFR,t = 1 / (1 + R)t

which stands for Present Value Interest Factor

PVIFAR,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(PVIFA10.6%,9) + $1,000(PVIF10.6%,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

9

10.6%

±$86

±$1,000

N

I/Y

PV

PMT

FV

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.

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.

2nd BGN  2nd SET

Enter

79

±$43,500

$740

N

I/Y

PV

PMT

FV

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:

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

1.0096t = 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

N

I/Y

PV

PMT

FV

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.

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

N

I/Y

PV

PMT

FV

Solve for

$7,090.44

Enter

8 × 365

5.9% / 365

±$5,600

N

I/Y

PV

PMT

FV

Solve for

$8,977.56

Enter

16 × 365

5.9% / 365

±$5,600

N

I/Y

PV

PMT

FV

Solve for

$14,392.26

What is the future value of $1,730 in 15 years assuming an interest rate of 7.00 percent compounded

What is the future value of $1,730 in 15 years assuming an interest rate of 7.00 percent compounded semiannually? (Do not include the dollar sign ($). 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).)

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 semiannually. To account for this, we will divide the interest rate by two (the number of compounding periods in a year), and multiply the number of periods by two. Doing so, we get:

FV = $1,730[1 + (0.0700/2)]30

FV = $4,855.75

Calculator Solution:

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

Enter

15 × 2

7.00% / 2

±$1,730

N

I/Y

PV

PMT

FV

Solve for

$4,855.75