Question

parts a-c

Coupon Bond

Note: You need to use a financial calculator or Excel to solve c. and g. in this problem. Provide the direct answer

to the question

and be sure to list all of the inputs to the calculator or Excel that were necessary to arrive at

your answer.

Consider a $6,000 8-yr coupon bond with a 3.5% coupon rate.

a.

What price can this bond be purchased for if the market interest rate is 5%? (answer in long form)

b.

If this bond is purchased for $5,000, what is the current yield?

c.

If this bond is purchased for $5,000, what is its yield to maturity (YTM)?

d.

Explain why the Current Yield is either greater than or less than the coupon rate.

e.

Explain why the YTM is either greater than or less than the current yield.

f.

After five years, the market interest rate has fallen to 2%. How much can this bond be sold for? (Answer in

long form.)

g.

Compute the original owner’s holding period return if the bond is originally purchased for $4,700.

Answer 1

Consider a $6,000 8-yr coupon bond with a 3.5% coupon rate.

1. What price can this bond be purchased for if the market interest rate is 5%? (answer in long form)

Bond price P0 = C* [1- 1/ (1+i) ^n] /i + M / (1+i) ^n

Where,

Price of the bond P0 =?

M = value at maturity, or par value = $6000

C = coupon payment or annual interest payment = 3.50% per annum, therefore coupon payment = 3.5% of $6000 = $210

n = number of payments = 8

i = yield to maturity or the market interest rate = 5% per year

Now we have,

P0 = $210 * [1 – 1 / (1+5%) ^8] /5% + 6000 / (1+5%) ^8

= $1,357.27 + $4,061.04

= $5,418.31

2. If this bond is purchased for $5,000, what is the current yield?

Current yield = annual coupon payment / market price of bond

Where,

Annual coupon payment = 3.5% of $6000 = $210

Market price of bond = $5,000

Therefore,

Current yield = $210 / $5,000 = 0.042 or 4.2%

3. If this bond is purchased for $5,000, what is its yield to maturity (YTM)?

We have following formula for calculation of bond’s yield to maturity

Bond price P0 = C* [1- 1/ (1+YTM) ^n] /YTM + M / (1+YTM) ^n

Where

Price of the bond P0 = $5,000

M = value at maturity, or par value = $6,000

C = coupon payment = 3.5% of $6000 = $210

Time period n = 8 years

Yield to maturity YTM =?

Therefore,

$5,000 = $210 * [1 – 1 / (1+YTM) ^8] / YTM + $6,000 / (1+YTM) ^8

By trial and error method we got the value of YTM = 6.21%

Therefore yield to maturity of bond is 6.21%.