Question
In: Finance
4. Refer to Table 10-1, which is based on bonds paying 10 percent interest for 20...
4. Refer to Table 10-1, which is based on bonds paying 10 percent interest for 20 years. Assume interest rates in the market (yield to maturity) decline from 16 percent to 6 percent.
a. What is the bond price at 16 percent?
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b. What is the bond price at 6 percent?
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c. What would be your percentage return on investment if you bought when rates were 16 percent and sold when rates were 6 percent? (Do not round intermediate calculations. Input your answer as a percent rounded to 2 decimal places.)
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Solutions
Expert Solution
(a)-Price of the Bond at 16%
The Market Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value
Face Value of the bond = $1,000
Annual Coupon Amount = $100 [$1,000 x 10%]
Annual Yield to Maturity = 16.00%
Maturity Period = 20 Years
Therefore, the Market Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value
= $100[PVIFA 16.00%, 20 Years] + $1,000[PVIF 16.00%, 20 Years]
= [$100 x 5.92884] + [$1,000 x 0.05139]
= $592.88 + $51.39
= $644.27
(b)-Price of the Bond at 6%
The Market Price of the Bond is the Present Value of the Coupon Payments plus the Present Value of the face Value
Face Value of the bond = $1,000
Annual Coupon Amount = $100 [$1,000 x 10%]
Annual Yield to Maturity = 6.00%
Maturity Period = 20 Years
Therefore, the Market Price of the Bond = Present Value of the Coupon Payments + Present Value of the face Value
= $100[PVIFA 6.00%, 20 Years] + $1,000[PVIF 6.00%, 20 Years]
= [$100 x 11.46992] + [$1,000 x 0.31180]
= $1,147.00 + $311.80
= $1,458.80
(c)-Return on Investment
Return on Investment = [(Price at 6% - Price at 16%) / Price at 16%] x 100
= [($1,458.80 - $644.27) / $644.27] x 100
= [$814.53 / $644.27] x 100
= 126.43%
NOTE
-The formula for calculating the Present Value Annuity Inflow Factor (PVIFA) is [{1 - (1 / (1 + r)n} / r], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.
-The formula for calculating the Present Value Inflow Factor (PVIF) is [1 / (1 + r)n], where “r” is the Yield to Maturity of the Bond and “n” is the number of maturity periods of the Bond.
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