Question

Serdang Corp. is considering an engineering project that requires an investment of RM220,000 and is expected to generate the following stream of payments (income) in the future.

                          Year         Payment

                           1              RM63,000

                           2              RM69,500

                           3              RM32,900

                           4              RM79,750

                           5              RM62,400

                           6              RM38,550

a.   If the cost of capital is 15%, does the present value of expected cash inflows exceed the value of the investment that has to be made today?

b.   Use linear interpolation method to find the interest rate at which the company would be just indifferent to the project.

c. Find the discounted payback period.

Answer 1

(a) Calculation of present value of cash inflows

Year	Cash inflows	PVF @ 15%	P.V.
1	63,000	0.869565217	54,782.61
2	69,500	0.756143667	52,551.98
3	32,900	0.657516232	21,632.28
4	79,750	0.571753246	45,597.32
5	62,400	0.497176735	31,023.83
6	38,550	0.432327596	16,666.23
		TOTAL	222,254.26

Since investment to be made today = $2,20,000, so P.V. of cash inflows exceed initial investment by $2,254.26 (222,254.26 - 220,000)

(b) Under interpolation method we shall assume two rates like 15% and 16%

Now NPV @15% calculated above = +2254.26

Year	Cash inflows	PVF @ 16%	P.V.
1	63,000	0.862068966	54,310.34
2	69,500	0.743162901	51,649.82
3	32,900	0.640657674	21,077.64
4	79,750	0.552291098	44,045.22
5	62,400	0.476113015	29,709.45
6	38,550	0.410442255	15,822.55
		TOTAL	216,615.02
		Initial investment	(220,000.00)
		NPV	(3,384.98)

interest rate at which the company would be just indifferent to the project. = IRR = LOWER RATE + {NPV(L) / NPV(L)- NPV(H)} * (HIGHER RATE - LOWER RATE)

IRR = 15% + [ 2254.26/ {2254.26- (-3384.98) } ] * (16 - 15) = 15% + (2254.26 / 5639.24) * 1

IRR = 15.40% approximately

interest rate at which the company would be just indifferent to the project = 15.40%

(c) Discounted payback period

Year	Cash inflows	PVF @ 15%	P.V.	Cumulative disc. CF
1	63,000	0.86956522	54,782.61	54,782.61
2	69,500	0.75614367	52,551.98	107,334.59
3	32,900	0.65751623	21,632.28	128,966.88
4	79,750	0.57175325	45,597.32	174,564.20
5	62,400	0.49717674	31,023.83	205,588.03
6	38,550	0.4323276	16,666.23	222,254.26

discounted payback period = 5 years + (222,254.26 - 220,000) / 16,666.23 = 5.14 years

discounted payback period = 5.14 years