Question

Four years ago, Candy Land Corp. issued a bond with a 14% coupon rate, semi-annual coupon payments, $1,000 face value, and 14-years until maturity.

1. a) You bought this bond three years ago (right after the bond made its coupon payment) when the yield-to-

   maturity was 10%. How much did you pay for the bond?

2. b) The current yield-to-maturity is 15%. If you sell the bond today (next coupon payment is in 6 months from

   today), after having owned it for three years, what would be your capital gain/loss yield? Remember, the capital

   gain/loss yield is the return resulting from price changes of your investment.

3. c) Suppose two years from now (right after the bond made its coupon payment) the bond has a value of $1,154.

   What would be the yield-to-maturity of the bond (APR, semi-annually compounded)? Use Excel or a financial calculator to solve this question.

Answer 1

Answer a.

Face value = $1,000

Semi-annual coupon amount = 1000 * 14% /2 = $70

Life of bond = 14 years

Bond was issued 4 years ago and was purchased 3 years ago.

Time to maturity when purchased = 13 years = 13 * 2 = 26 semi-annual periods

Semi-annual yield to maturity = 10%/2 = 5%

To get price paid we use PV function of excel:

PV (rate, nper, pmt, fv, type)

= PV (5%, 26, -70, -1000,0)

= $1287.5037

Price paid = $1,287.50

Answer b:

At Current:

Semi-annual yield to maturity =15%/ 2 = 7.5%

Time to maturity = 10 years = 10 * 2 = 20 semi-annual periods

Price = PV (7.5%, 20, 70, -1000, 0)

= $949.03

Capital loss = $949.03 - $1,287.50 = $338.47

Current price = $949.03

Capital loss = $338.47

Answer c:

Two years from now the bond has a value = $1,154

Time to maturity = 16 semiannual periods

To get yield to maturity, we use RATE function of excel:

= RATE (nper, pmt, pv, fv, type)

= RATE (16, 70, -1154, 1000, 0)

= 5.525%

Yield to maturity = 5.525% * 2 = 11.05%

Yield to maturity = 11.05%