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# TVM, Bonds (pricing, yields)

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Please answer the following finance problems in detail and not just the steps that you take to arrive at the answer, Thanks!

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

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

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

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

4) 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 36, 37)

5) Bond Pricing. If Circular File wants to issue a new 6-year bond at face value, what coupon rate must the bond offer?(A 6-year Circular File bond pays interest of \$80 annually and sells for \$950. What is its coupon rate, current yield, and yield to maturity?)

6) Bond Yields. An AT&T bond has 10 years until maturity, a coupon rate of 8 percent, and sells for \$1,100.

a.What is the current yield on the bond?
b.What is the yield to maturity?

7) Bond Prices and Yields.

a.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?

b.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?

#### Solution Preview

Note: The abbreviations have the following meanings

PVIF= Present Value Interest Factor
PVIFA= Present Value Interest Factor for an Annuity
FVIF= Future Value Interest Factor
FVIFA= Future Value Interest Factor for an Annuity

They can be read from tables or calculated using the following equations
PVIFA( n, r%)= =[1-1/(1+r%)^n]/r%
PVIF( n, r%)= =1/(1+r%)^n
FVIF( n, r%)= =(1+r%)^n
FVIFA( n, r%)= =[(1+r%)^n -1]/r%

Please answer the following finance problems in detail and not just the steps that you take to arrive at the answer, Thanks!

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

Here we are being asked to find the present value (PV) (at time 0) of a cash flow occuring in future

A) n= 10
r= 8.00%
PVIF (10 periods, 8.% rate ) = 0.463193
Therefore PV= \$46.32 =0.463193 x \$100

B) n= 20
r= 8.00%
PVIF (20 periods, 8.% rate ) = 0.214548
Therefore PV= \$21.45 =0.214548 x \$100

C) n= 10
r= 4.00%
PVIF (10 periods, 4.% rate ) = 0.675564
Therefore PV= \$67.56 =0.675564 x \$100

D) n= 20
r= 4.00%
PVIF (20 periods, 4.% rate ) = 0.456387
Therefore PV= \$45.64 =0.456387 x \$100

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

A .r = 8 percent. t = 10 years.
B. r = 8 percent. t = 20 years.
C .r = 4 percent. t = 10 years.
D. r = 4 percent. t = 20 years.

Here we are being asked to find the future value (FV) of a cash flow occuring now (at time 0)

A) n= 10
r= 8.00%
FVIF (10 periods, 8.% rate ) = 2.158925
Amount = \$100
Therefore FV= \$215.89 =2.158925 x ...

#### Solution Summary

Answers to questions on Time Value of Money (Present values, Future Values, Interest rate), Loan payments, Bond Pricing, Bond yields

\$2.19