Question

(Bond valuation​ relationships) A bond of Telink Corporation pays ​$110 in annual​ interest, with a ​$1,000 par value. The bonds mature in 30 years. The​ market's required yield to maturity on a​ comparable-risk bond is 88 percent.

a.  What is the value of the bond if the​ market's required yield to maturity on a​ comparable-risk bond is 88 ​percent?

(Round to the nearest​ cent.)

b. ​(i) What is the value of the bond if the​ market's required yield to maturity on a comparable risk bond increases to 12 ​percent? 

​(Round to the nearest​ cent.)

b. ​(ii) What is the value of the bond if the​ market's required yield to maturity on a comparable risk bond decreases to 55 ​percent?

​ (Round to the nearest​ cent.)

c.  The change in the value of a bond caused by changing interest rates is called​ interest-rate risk. Based on the answers in part (b):

A decrease in interest rates​ (the yield to​ maturity) will cause the value of a bond to:

(increase, be unchanged, or decrease)?

By​ contrast, an increase in interest rates will cause the value to:

(increase, be unchanged, or decrease)?

Also, based on the answers in part (b)​

If the yield to maturity​ (current interest​ rate):

Equals the coupon interest​ rate, the bond will sell at (par, a discount, a premium)?

Exceeds the​ bond's coupon​ rate, the bond will sell at (par, a discount, a premium)?

​Is less than the​ bond's coupon​ rate, the bond will sell at (par, a discount, a premium)?

Answer 1

1. Value of the bond can be calculated in following manner

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

Where,

M = value at maturity, or par value = $ 1000

P0 = the current market price of bond =?

C = coupon payment =11% of $1,000 = $110

n = time to maturity or number of payments = 30 (years)

YTM = interest rate, or yield to maturity =88% (for similar risk bonds)

Now we have,

P0 = $110 * [1 – 1 / (1+88%) ^30] /88% + $1000 / (1+88%) ^30

Or P0 = $125.00 + $0.00

= $125.00

Price of the bond of Telink Corporation is $125.00

2. ​(i) What is the value of the bond if the​ market's required yield to maturity on a comparable risk bond increases to 12 ​percent? 

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

Where,

M = value at maturity, or par value = $ 1000

P0 = the current market price of bond =?

C = coupon payment =11% of $1,000 = $110

n = time to maturity or number of payments = 30 (years)

YTM = interest rate, or yield to maturity =12% (for similar risk bonds)

Now we have,

P0 = $110 * [1 – 1 / (1+12%) ^30] /12% + $1000 / (1+12%) ^30

Or P0 = $886.07 + $33.38

= $919.45

Price of the bond of Telink Corporation is $919.45

​

2. (ii) What is the value of the bond if the​ market's required yield to maturity on a comparable risk bond decreases to 55 ​percent?

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

Where,

M = value at maturity, or par value = $ 1000

P0 = the current market price of bond =?

C = coupon payment =11% of $1,000 = $110

n = time to maturity or number of payments = 30 (years)

YTM = interest rate, or yield to maturity =55% (for similar risk bonds)

Now we have,

P0 = $110 * [1 – 1 / (1+55%) ^30] /55% + $1000 / (1+55%) ^30

Or P0 = $200.00 + $0.002

= $200.002

Price of the bond of Telink Corporation is $200.00

3. The change in the value of a bond caused by changing interest rates is called​ interest-rate risk. Based on the answers in part (b):

A decrease in interest rates​ (the yield to​ maturity) will cause the value of a bond to: increase

By ​contrast, an increase in interest rates will cause the value to: decrease

Also, based on the answers in part (b)​

If the yield to maturity ​(current interest​ rate):

Equals the coupon interest ​rate, the bond will sell at par

Exceeds the​ bond's coupon​ rate, the bond will sell at a discount

​Is less than the​ bond's coupon​ rate, the bond will sell at a premium