Question

If P = -$500,000, Annual Income = +$10,000 per year, Salvage= +$700,000, and N = 10 years. Determine the Interest Rate

Answer 1

Trial and error method is used here for calculating the interest rate.

This is the interest rate at which the present value of cash inflow is equal to initial cost (P).

Since salvage value (700,000) is above the initial cost (500,000), the interest rate should not be very high; this may be within 10%. Therefore, for trial and error we take two rates initially – 2% and 8%. If the required rate is not found in between, another rate (s) could be taken.

Table

Year	CF	2% factors = 1/1.02^year	PV = CF × 2% factor	8% factors = 1/1.08^year	PV = CF × 2% factor
0	-500,000	1/1.02^0 = 1	-500,000	1	-500,000
1	10,000	1/1.02^1 = 0.9804	9,804	0.9259	9259
2	10,000	1/1.02^2 = 0.9612	9,612	0.8573	8573
3	10,000	0.9423	9,423	0.7938	7938
4	10,000	0.9238	9,238	0.7350	7350
5	10,000	0.9057	9,057	0.6806	6806
6	10,000	0.8880	8,880	0.6302	6302
7	10,000	0.8706	8,706	0.5835	5835
8	10,000	0.8535	8,535	0.5403	5403
9	10,000	0.8368	8,368	0.5002	5002
10	710,000	0.8203	582,413	0.4632	328,872
Total			164,036		-108,660

     

Rate of interest is in between positive value to negative value.

Hence, by the use of interpolation formula as below:

Rate of interest = rate at which NPV is positive + [NPV at 2% rate / (NPV at 2% - NPV at 8%)] × Difference in rates

                        = 2% + [164,036 / (164,036 + 108,660)] × (8 – 2)

                        = 2% + [164,036 / 272,696] × 6

                        = 2% + 0.6015 × 6

                        = 2% + 3.60

                        = 5.60% (Answer)