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.
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 |
1. Present value of an annuity On January 1, you win $34,500,000 in the state lottery....
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