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# Important information about Present Value Analysis

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Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times:
1. r = 8 percent, t = 10 years.
2. r = 8 percent, t = 20 years.
3. r = 4 percent, t = 10 years.
4. r = 4 percent, t = 20 years.

Future Values. Compute the future value of a \$100 cash flow for the same combinations of rates and times as in problem 1.

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Time period
\$400 11 \$684
\$183 4 \$249
\$300 7 \$300

Loan Payments. If you take out an \$8,000 car loan that calls for 48 monthly payments at an APR of 10 percent, what is your monthly payment? What is the effective annual interest rate on the loan?
(using the excel PMT function)

Amortizing Loan. You take out a 30-year \$100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan?

Amortizing Loan. Consider a 4-year amortizing loan. You borrow \$1,000 initially, and repay it in four equal annual year-end payments.

1. If the interest rate is 8 percent, show that the annual payment is \$301.92.
2. Fill in the following table, which shows how much of each payment is interest versus principal repayment (that is, amortization), and the outstanding balance on the loan at each date.

Bond Yields. A bond with face value \$1,000 has a current yield of 7 percent and a coupon rate of 8 percent. What is the bond's price?

Bond Pricing. A 6-year Circular File bond pays interest of \$80 annually and sells for \$950. What are its coupon rate, current yield, and yield to maturity?

Bond Prices and Yields.

1. Several years ago, Castles in the Sand, Inc., issued bonds at face value at a yield to maturity of 7 percent. Now, with 8 years left until the maturity of the bonds, the company has run into hard times and the yield to maturity on the bonds has increased to 15 percent. What has happened to the price of the bond?
2. Suppose that investors believe that Castles can make good on the promised coupon payments, but that the company will go bankrupt when the bond matures and the principal comes due. The expectation is that investors will receive only 80 percent of face value at maturity. If they buy the bond today, what yield to maturity do they expect to receive?

A project has a cost (projected outflow of (\$14,000) in year 0.
This project has the following projected inflows in years 1-5:
Year 1 \$ 2,000
Year 2 \$ 4,000
Year 3 \$ 7,000
Year 4 \$ 7,000
Year 5 \$ 7,000

Ø When is the pay back? (Year / months):

Ø If this firm has a payback policy of 3 years, will this project meet that criteria?:

Consider the data on the following two mutually exclusive projects under consideration by the Stephen Company:

Year

Project A

Project B
0

-30,000

-60,000
1

10,000

20,000
2

10,000

20,000
3

10,000

20,000
4

10,000

20,000
5

10,000

20,000
The cost of capital is 14%.
Given this information, calculate the following values for each project using the time value tables in the text:
Ø NPV
Ø IRR (Round to the nearest whole percentage.)
Ø Profitability index
Ø Payback period

#### Solution Preview

Present Values. Compute the present value of a \$100 cash flow for the following combinations of discount rates and times:
1. r = 8 percent, t = 10 years.
2. r = 8 percent, t = 20 years.
3. r = 4 percent, t = 10 years.
4. r = 4 percent, t = 20 years.

PV = FV/(1 + i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period
1. PV = 100/(1 + 0.08)10
PV = 46.32
2. PV = 100/(1 + 0.08)20
PV = 21.45
3. PV = 100/(1 + 0.04)10
PV = 67.56
4. PV = 100/(1 + 0.04)20
PV = 45.64

Future Values. Compute the future value of a \$100 cash flow for the same combinations of rates and times as in problem 1.

FV = PV (1+i)n where PV is the present value
FV is the future value
i is the interest rate
n is the period

1. FV = 100(1 + 0.08)10
FV = 215.89

2. FV = 100(1 + 0.08)20
FV = 466.10

3. FV = 100(1 + 0.04)10
FV = 148.02

4. FV = 100(1 + 0.04)20
FV = 219.11

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values:

Present Value Years Time period
\$400 11 \$684
\$183 4 \$249
\$300 7 \$300

400 = 684/(1 + i)11
(1 + i)11/11 = (1.71)1/11

i = 5.00

183 = 249/(1 + i)4
(1 + i)4/4 = (1.3607)1/4

i = 8.00

300 = 300/(1 + i)7
(1 + i)7/7 = (1)1/7

i = 0.00

Loan Payments. If you take out an \$8,000 car loan that calls for 48 monthly payments at an APR of 10 percent, what is your monthly payment? What is the effective annual interest rate on the loan?
(using the excel PMT function) please refer to excel file.

Effective annual interest rate
= (1 + 0.10)12 - 1 = 10.47%
12

Amortizing Loan. You take out a 30-year \$100,000 mortgage loan with an APR of 6 percent and monthly payments. In 12 years you decide to sell your house and pay off the mortgage. What is the principal balance on the loan? please refer to excel file.

79,089.55

Amortizing Loan. Consider a 4-year ...

#### Solution Summary

This solution is comprised of a detailed explanation to calculate the present values, the bond price, and the NPV, payback, and IRR of the projects.

\$2.19