Question

Smith agrees to pay Jones $13,207 after ten years in exchange for Jones paying Smith $1,000 at the beginning of each year for ten years. Just after the 6th payment, Jones decides he cannot continue payments and offers Smith the following three alternatives:

1. Stop payments. Smith pays Jones $8,500 at the end of the original ten-year period.

2. Stop payments. Smith pays Jones $7,000 now and closes the transaction.

3. Continue payments, but at $500 per year. Smith pays Jones $10,500 at the end of the original 10-year period.

Which if any of the alternatives could Smith accept if he is to pay no more than the effective rate of interest agreed upon initially?

Answer 1

This IRR method is useful for getting exact interest rate with decimals also which is hard to find manual test.

(You have to take the lower and higher interest rates in such a way that the required NPV/Maturity value should fall in between the lower and higher NPV/Maturity value)

By cross verification through test checking different rates of interests, we can find the effective rate of interest for the transaction as 5%.(Follow whichever method you feel easier).

At the end of 6th payment, the balance available with Smith along with accrued interest is 1000*(6.802)=6802

Alternative 1: The available amount with Smith of 6802 at the end of 10 year Period with no further payments will be 6802*(1.2763)=8681

If Smith pays Jones 8500, the Profit he retains is (8681-8500)=181.

Alternative 2: If Smith pays 7000 now, he has to incur loss of (6802-7000)=198.

Alternative 3: Further payments will be 500 only. Hence at the end of 5 years from now, The Balance with Smith will be 8681 (as per alternative 1) plus 500(4.5256)=10944.

If he pays 10500, he can retain profit of 444.

Hence alternative 3 is most beneficial for Smith.