Assignment: Present Value Applications
1. What dollar amount (principal) deposited now earning interest at the rate of 6% compounded annually would grow to $100,000 four years from now? What would be the amount of interest earned in each year?
2. You are given a choice of being paid either $18,000 now or $20,000 two years from now. Which would you rather have, assuming you could earn 10% interest on any cash you have now?
3. Assume that a company buys a machine and signs a note agreeing to pay $200,000 at the end of two years. This $200,000 payment includes the cost of the machine (principal) plus 10% annual interest.
a. What is the cost of the machine?
b. What would the company record as interest expense in the first year?
c. How would the note payable appear on the company's balance sheet at the end of the first year?
d. What is the company's interest expense for the second year?
e. What would be the cost of the machine if, in addition to signing the note, the company had made a cash down payment of $50,000?
4. Would you be better off accepting $27,000 now or $10,000 at the end of each of the next three years, assuming that you can earn interest at 1) 6%? or 2) 4%?
5. Assume that a company sold an asset and the buyer signed a note agreeing to pay $50,000 at the end of every year for 3 years. The three $50,000 payments include the original principal or amount borrowed plus interest on the unpaid balance at the beginning of each year of 12%.
a. What is the selling price of the asset?
b. How much interest revenue does the company earn in the first year? The second year? The third year?
c. How would the note receivable appear on the balance sheet at the end of the first year? The second year?
d. What would the selling price of the asset have been if, in addition to the note, the buyer had been required to pay a $20,000 cash down payment?
6. An investor has $100,000 to invest for a period of 12 years and he desires an accumulation of $200,000 at the end of the period. Approximately what rate of compound interest must his money earn?
7. An investor has $300,000 to invest at 16% annual interest, compounded quarterly, and he desires an accumulation of $600,000 at the end of the period. Approximately how many years will be required?
8. A company buys some new office equipment and agrees to pay it off in 24 -monthly payments of $20,000 each, beginning at the end of the first month. The payments included 24% annual interest on the unpaid loan balance as of the beginning of each month.
a. What is the cost of the office equipment? (Remember, monthly compounding!)
b. What is the interest expense for the first month? The second? The third?
9. Another company leases a building, agreeing to pay $1,000,000 at the end of every 3 months (quarterly) for 5 years (i.e., a total of 20 payments).
a. Compute lease expense of the first year if this is an operating lease.
b. What if the terms of the lease are such that the lease must be capitalized; that is, the company must show both the asset and the liability on its balance sheet. If the interest rate is 16%, compute the recorded cost of the leased asset, the interest expense for the first year and depreciation expense for the first year (assuming straight-line, no residual value, and a 5 year estimated life).
c. As the manager of the firm, which of the two reporting methods most favorably reflects the company's operations?
d. How would the answers to a. and b. above change if the lease payment is made at the beginning of each quarter?
10. Find the present values for each of the following sets (A - F) of dollar payments if the discount rate is (a) 10%, (b) 15%.
Received at Beginning of Year A B C D E F
1 0 1,000 1,500 0 4,000 1,000
2 1,000 1,000 1,500 2,000 3,000 3,000
3 1,000 1,000 2,000 2,000 3,000 3,000
4 1,000 1,000 2,000 2,000 3,000 3,000
5 1,000 0 2,000 2,000 3,000 0
6 0 0 0 5,000 4,000 5,000
11. Joe wins the $50,000,000 Texas lottery. He receives $5,000,000 today and $2,500,000 at the end of the next 18 years. Assuming Joe could earn 8%, how much is his prize worth?