Question

appendix 1 ex 11 - 12 present value of bonds payable; discount
pinder co. produces and sells high - quality video equipment. to finance its operations, pinder issued $25,000,000 of five - year, 7% bonds, with interest payable semiannually, at a market (effective) interest rate of 9%. determine the present value of the bonds payable, using the present value tables in exhibits 5 and 7. round to the nearest dollar.
bonds payable proceeds where market rate > contract rate
issue date: jan 1
face: $25,000,000
term: 5 years
contract rate: 7% ( % semiannual)
market rate: 9% ( % semiannual)
declare: premium or discount
cash per contract market factor (i = %;n = ) present value
principal: × = $
interest: × =
bond proceeds $
face - proceeds =
entry at issue date
jan 1

Explanation:

Step1: Calculate semi - annual interest payment

The face value of the bonds is $F = 25000000$, and the annual contract rate is 7%. The semi - annual contract rate $r=\frac{7\%}{2}=3.5\%$. So the semi - annual interest payment $I = F\times r=25000000\times0.035 = 875000$.

Step2: Determine the number of periods and semi - annual interest rate

The bond term is 5 years, and since interest is paid semi - annually, the number of periods $n = 5\times2=10$. The semi - annual market interest rate $i=\frac{9\%}{2}=4.5\%$.

Step3: Calculate the present value of the principal

Using the present - value of a single amount table (Exhibits 5 and 7), the present - value factor for $i = 4.5\%$ and $n = 10$ is $PVF_{1}=0.643928$. The present value of the principal $PV_{principal}=F\times PVF_{1}=25000000\times0.643928 = 16098200$.

Step4: Calculate the present value of the interest payments

Using the present - value of an ordinary annuity table, the present - value factor for $i = 4.5\%$ and $n = 10$ is $PVF_{2}=7.91271$. The present value of the interest payments $PV_{interest}=I\times PVF_{2}=875000\times7.91271 = 6923611.25$.

Step5: Calculate the present value of the bonds payable

The present value of the bonds payable $PV = PV_{principal}+PV_{interest}=16098200 + 6923611.25=23021811.25\approx23021811$.

Step6: Determine premium or discount

Since the market rate (9% annual, 4.5% semi - annual) is greater than the contract rate (7% annual, 3.5% semi - annual), the bonds are issued at a discount. The discount amount is $25000000 - 23021811=1978189$.

Answer:

The present value of the bonds payable is $23021811$. The bonds are issued at a discount.
Entry at issue date (assuming a simple journal entry for bond issuance):
Debit: Cash $23021811$
Debit: Discount on Bonds Payable $1978189$
Credit: Bonds Payable $25000000$