Question

1. MAX holds bonds with a face value of 1,000,000$, an 8% interest rate (payment once a year) and a remaining maturity of four years. Answer the following question.
(1) If the market price of the bond is 1,150,000$, what is the maturity yield on the bond?
(2) If the maturity yield on the bond is 10%, what is the appropriate price for this bond?
(3) Assuming that you pay this ticket twice a year, put in preceding questions (1), (2).

Answer 1

Answer 1.

Face Value = $1,000,000
Current Price = $1,150,000

Annual Coupon Rate = 8.00%
Annual Coupon = 8.00% * $1,000,000
Annual Coupon = $80,000

Time to Maturity = 4 years

Let Annual YTM be i%

$1,150,000 = $80,000 * PVIFA(i%, 4) + $1,000,000 * PVIF(i%, 4)

Using financial calculator:
N = 4
PV = -1150000
PMT = 80000
FV = 1000000

I = 3.88%

Annual Yield to Maturity = 3.88%

Answer 2.

Face Value = $1,000,000
Annual Coupon = $80,000
Time to Maturity = 4 years
Market Yield = 10%

Bond Price = $80,000 * PVIFA(10%, 4) + $1,000,000 * PVIF(10%, 4)
Bond Price = $80,000 * (1 - (1/1.10)^4) / 0.10 + $1,000,000 / 1.10^4
Bond Price = $936,602.69

Answer 3.

Part (1):

Face Value = $1,000,000
Current Price = $1,150,000

Annual Coupon Rate = 8.00%
Semiannual Coupon Rate = 4.00%
Semiannual Coupon = 4.00% * $1,000,000
Semiannual Coupon = $40,000

Time to Maturity = 4 years
Semiannual Period = 8

Let Semiannual YTM be i%

$1,150,000 = $40,000 * PVIFA(i%, 8) + $1,000,000 * PVIF(i%, 8)

Using financial calculator:
N = 8
PV = -1150000
PMT = 40000
FV = 1000000

I = 1.956%

Semiannual Yield to Maturity = 1.956%
Annual Yield to Maturity = 2 * 1.956%
Annual Yield to Maturity = 3.91%

Part (2):

Face Value = $1,000,000
Semiannual Coupon = $40,000
Semiannual Period = 8 years
Annual Market Yield = 10%
Semiannual Market Yield = 5%

Bond Price = $40,000 * PVIFA(5%, 8) + $1,000,000 * PVIF(5%, 8)
Bond Price = $40,000 * (1 - (1/1.05)^8) / 0.05 + $1,000,000 / 1.05^8
Bond Price = $935,367.87