Question

Orlando Health System has bonds outstanding that have 8 years remaining to maturity, a coupon interest rate of 8% paid annually, and $1,000 par value.

a. What is the yield to maturity on the issue if the current market price is $1,124.00?

b. If the yield to maturity calculated in part a remains constant, what will happen to the value of the bonds as the maturity date approaches?

c. What is the yield to maturity on the issue if the current market price is $893.00?

d. If the yield to maturity calculated in part c remains constant, what will happen to the value of the bonds as the maturity date approaches?

Answer 1

Question - a

Face value of the bond = 1000, n = years to maturity = 8 and C = Coupon = 1000 * 8 % = $80

If ........ " r " is the YTM, then present value of future cash inflows must be equal to current market price of 1,124.

Price of the bond = C * [ 1 - (1+r)^-n ] / r + Face value * (1+r)^-n = 1124

80 * [ 1 - (1+r)^-8 ] / r + 1000 * (1+r)^-8 = 1124

For solving the value of......... " r " in the above equation we have to use trail and error technique.

First trail with ......... " r " = 5.80 %

80 * [ 1 - (1.058)^-8 ] / 0.058 + 1000 * (1.058)^-8 = 500.74 + 636.96 = 1137.7

Second trail with ........ " r " = 6.20 %

80 * [ 1 - (1.062)^-8 ] / 0.058 + 1000 * (1.062)^-8 = 492.87 + 618.02 = 1110.89

Now use the simple interpolation method to find the YTM = r

5.80 ..............1137.70

X ................1124

6.20...............1110.89

(X - 5.80) / ( 6.20 - 5.80) = ( 1124 - 1137.70 ) / ( 1110.89 - 1137.70)

X - 5.80 / 0.40 = - 13.70 / - 26.81

X - 5.80 = 0.20

X = 5.80 + 0.20 = 6 % ............ final answer

Question - b

In this case - (a), we see that bonds are premium bonds. Hence with YTM remaining constant up to maturity, bond price moves towards its face value. That means moves from 1124 to 1000. As such, we can say that value of bond decreases as the date of maturity approaches.

Question - c

If ........ " r " is the YTM, then present value of future cash inflows must be equal to current market price of 893

Price of the bond = C * [ 1 - (1+r)^-n ] / r + Face value * (1+r)^-n = 893

80 * [ 1 - (1+r)^-8 ] / r + 1000 * (1+r)^-8 = 893

For solving the value of......... " r " in the above equation we have to use trail and error technique.

First trail with ......... " r " = 9.80 %

80 * [ 1 - (1.098)^-8 ] / 0.098 + 1000 * (1.098)^-8 = 429.92 + 473.35 = 903.27

Second trail with ........ " r " = 10.20 %

80 * [ 1 - (1.102)^-8 ] / 0.102 + 1000 * (1.102)^-8 = 423.70 + 459.78 = 883.48

Now use the simple interpolation method to find the YTM = r

9.80 ..............903.27

X ................893

10.20............883.48

(X - 9.80) / ( 10.20 - 9.80) = ( 893 - 903.27 ) / ( 883.48 - 903.27)

X - 9.80 / 0.40 = - 10.27 / - 19.79

X - 9.80 = 0.21

X = 9.80 + 0.21 = 10.21 % ............ final answer

Question - d

In the case - (c), we see that the bonds are discount bonds. Therefore, with constant YTM over the life of bonds, price of the bond moves upwards to reach the face value of the bond. Hence we can say that value of bond increases as the date of maturity approaches.