Acompany must repay the bank a single payment of $20,000 cash in 3 years for a loan it entered into. the loan is at 8% interest compounded annually. the present value factor for 3 years at 8% is 0.7938. the present value of an annuity factor for 3 years at 8% is 2.5771. the present value of the loan:

Present value of the loan = $15,877

Explanation:

One thing that one must master with this type of question is how to choose between a present value factor and a present value annuity factor. If the solution to a question calls for discounting a single payment or a set of payments with different amounts, then one should use present value factors. If the question calls for discounting an annuity, which is a series of equal payments at equal intervals, then one should use a present value annuity factor.

In this question, the company must repay a single payment of $20,000 in 3 years. to find the present value we discount this payment that is to made at the end of year 3 by multiplying with the present value factor for 3 years at 8% is 0.7938 i.e

Alternatively one can use a tabular format to visualise what is happening as follows:

YearCash-flowPV factor at 8%Present value

1                -                              0.9259               $0.00  

2                -                             0.8573                $0.00  

3        $20,000                       0.7938             $15,876.64  

                          Present Value                       $15,876.64