8) Cheyenne Inc. is planning to issue bonds that will pay 9% semiannual interest

ID: 2485140 • Letter: 8

Question

8) Cheyenne Inc. is planning to issue bonds that will pay 9% semiannual interest and mature in 9 years.

a. How much will investors be willing to pay for a $1,000 bond if the prevailing market yield rate is 8%?

b. How much will investors be willing to pay for a $1,000 bond if the prevailing market interest rate is 10%?

Present value of $1: 4% 5% 6% 7% 8%

15 0.555 0.481 0.417 0.362 0.315

16 0.534 0.458 0.394 0.339 0.292

17 0.513 0.436 0.371 0.317 0.270

18 0.494 0.416 0.350 0.296 0.250

19 0.475 0.396 0.331 0.277 0.232

Present value of annuity of $1: 4% 5% 6% 7% 8%

15 11.118 10.380 9.712 9.108 8.559

16 11.652 10.838 10.106 9.447 8.851

17 12.166 11.274 10.477 9.763 9.122

18 12.659 11.690 10.828 10.059 9.372

19 13.134 12.085 11.158 10.336 9.604

Pricing formula:

Price = Coupon amount (PVIFA(Int. rate,No. of period) ) + Face Value (PVIF(Int. rate,No. of period) )

a) Being interest payment is half yearly so interest rate gets half and period gets doubled. Interest rate=8%

Price = (1000 * 4.5%) (PVIFA(4%,18) ) + 1000 (PVIF(4%,18) ) = 45 * 12.659 + 1000 * 0.494 = $ 1063.66

b) Interest rate being 10% per annum

Price = (1000 * 4.5%) (PVIFA(5%,18) ) + 1000 (PVIF(5%,18) ) = 45 * 11.690 + 1000 * 0.416 = $ 942.05

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