Question

1. Present value of an annuity On January 1, you win $34,500,000 in the state lottery. The $34,500,000 prize will be paid in equal installments of $5,750,000 over six years. The payments will be made on December 31 of each year, beginning on December 31 of this year. The current interest rate is 6%. This information has been collected in the Microsoft Excel Online file. Open the spreadsheet, perform the required analysis, and input your answers in the question below.

2. Pinder Co. produces and sells high-quality video equipment. To finance its operations, Pinder issued $28,000,000 of four-year, 5% bonds, with interest payable semiannually, at a market (effective) interest rate of 8%. This information has been collected in the Microsoft Excel Online file. Open the spreadsheet, perform the required analysis, and input your answers in the question below.

Answer 1

Solution to question 1
The present value factor can be taken from the present value table
The present value is the annual amount received x present value factor
Annual amount received	Present value factor	Present value
5,750,000	0.94340	5,424,528
5,750,000	0.89000	5,117,480
5,750,000	0.83962	4,827,811
5,750,000	0.79209	4,554,539
5,750,000	0.74726	4,296,734
5,750,000	0.70496	4,053,523
34,500,000		28,274,615	Present value of $34.5 million

Solution to question 2
Note we always use market rate to calculate the premium or discount.
Here market rate is higher so that bonds will need to be sold at a discount.
Interest payable semi-annually. Thus stated an market interest rate for half year is 2.5% and 4% respectively.
Here the number of years are not given. We are presuming it to be 5 years. As interest is semi-annual, this represents 10 periods.
Present value of principal (PV o $1 @4% and n=10 is .67556) = $28million * 0.67556 = $18,915,680
Present value of interest payments (PV of annuity @4% and n=10 is 8.111) = $28million * 2.5% * 8.111 = 5,677,700
Carrying value of the bond = $18,915,680 + 5,677,700 = $24,593,380
Discount = $28,000,000 - $24,593,380 = $3,406,620
The amortization would be as follows:
Period	Effective interest @4%	Interest paid at 2.5%	Plug for discount amortization	Bond carrying value
0	-	-	-	24,593,380
1	983,735	700,000	283,735	24,877,115
2	995,085	700,000	295,085	25,172,200
3	1,006,888	700,000	306,888	25,479,088
4	1,019,164	700,000	319,164	25,798,251
5	1,031,930	700,000	331,930	26,130,181
6	1,045,207	700,000	345,207	26,475,389
7	1,059,016	700,000	359,016	26,834,404
8	1,073,376	700,000	373,376	27,207,780
9	1,088,311	700,000	388,311	27,596,092
10	1,103,844	700,000	403,844	27,999,935
				The difference of $65 is due to rounding