Question

(a) Calculate the net present value (NPV) of a project which requires an initial investment of $243,000 and it is expected to generate a cash inflow of $58,000 each month for 12 months. Assume that the salvage value of the project is zero. The target rate of return is 12 % per annum.
(b) An initial investment of $8,720 thousand (i.e. × 1,000) on plant and machinery is expected to generate cash inflows of $3,411 thousand, $4,070 thousand, $5,824 thousand and $2,065 thousand at the end of first, second, third and fourth year respectively. At the end of the fourth year, the machinery will be sold for $900 thousand. Calculate the net present value (NPV) of the investment if the discount rate is 18 %. Round-off your final numerical answer to the nearest thousand dollars.
(c) Suppose you make an annual contribution of $20,000 to your investment-linked product account at the beginning of each year for five years. If your investment provides 16 % annual returns to your investment, what is your asset value (by annual-compounding) in your account at the end of five years? Also, draw the corresponding cash flow diagram with all key labels indicated clearly.
(d) With reference to part (c), assume the investment-linked product account will keep running without any further contribution and the annual return keep 16 % pa. If you withdraw $80,000 at the 8th year (after interest compounding), what is your account value at the end of 10th year?

Answer 1

(a) Initial Investment = $243,000

Net Cash Inflow per Period = $58,000

Number of Periods = 12

Discount Rate per Period = 12% ÷ 12 = 1%

Net Present Value = $58,000 ×(1 −(1 + 1%)^-12) ÷ 1% −$243,000

= $58,000 ×(1 −1.01^-12) ÷ 0.01 −$243,000

≈ $58,000 ×(1 −0.887449) ÷ 0.01 −$243,000

≈ $58,000 ×0.112551 ÷ 0.01 −$243,000

≈$58,000 ×11.2551 −$243,000

≈ $652,795.8 −$243,000

≈ $409,795.8

(b) PV Factors:

Year 1 = 1 ÷ (1 + 18%)¹ ≈ 0.8475

Year 2 = 1 ÷ (1 + 18%)² ≈ 0.7182

Year 3 = 1 ÷ (1 + 18%)³ ≈ 0.6086

Year 4 = 1 ÷ (1 + 18%)⁴ ≈ 0.5158

Calculation of net present value -

Year	1	2	3	4
Net Cash Inflow	$3,411	$4,070	$5,824	$2,065
Salvage Value				$900
Total Cash Inflow	$3,411	$4,070	$5,824	$2,965
*Present Value Factor	0.8475	0.7182	0.6086	0.5158
Present Value of Cash Flows	$2,890.68	$2,923.01	$3,544.67	$1,529.31
Total PV of Cash Inflows	$10,888
−Initial Investment	−8,320

Net Present Value $2,568 Thousand