Question

Using information about the estimated costs, estimated benefits and a discount rate of 9% for Project XYZ, calculate the discount factor for each year, the discounted costs, the discounted benefits, the return-on-investment (ROI) and the net-present value (NPV). In which year does the payback occurs? Total | O 175,000 ? ? Estimated Costs Discount Factor Discounted Costs | 22.500,7 22,500 ? ? Year 2 | 22,500 ? ? 3 | 22,500 ? ? 4 22,500 ? ? | 5 | 22,500 ? ? ? 80.000 80.000 Estimated Benefits Discount Factor Discounted Benefits 80,000 ? ? 80.000 ? ? 80.000 ? ? ? ? ? Discounted Benefits - Costs Cumulative Benefits - Costs Return on Investment (ROI)

Answer 1

	Year						Total
	0	1	2	3	4	5
Estimated Costs	175,000	22,500	22,500	22,500	22,500	22,500	287,500
Discount Factor	1.0	1.09	1.188	1.295	1.412	1.539
Discounted Costs	175,000	20,642	18,938	17,374	15,940	14,623	262,517
Estimated Benefits	0	80,000	80,000	80,000	80,000	80,000
Discount Factor	1.0	1.09	1.188	1.295	1.412	1.539
Discounted Benefits	0	73,394	67,334	61,775	56,674	51,995	311,172
Estimated Benefits - Estimated Costs	-175,000	57,500	57,500	57,500	57,500	57,500	112,500
Cumulative (Estimated Benefits - Estimated Costs)	-175,5000	-117,500	-60,000	-2,500	55,000	112,500
Discounted Benefits - Discounted Costs	-175,500	52,752	48,397	44,401	40,734	37,371	48,655

Discount rate is 9%

$Discount\ factor\ for\ 'n'\ year\ = (1+0.09)^{n}$

$Discounted\ Costs= \frac{Estimated\ Costs}{Discount\ Factor}\\ \\Discounted\ Benefits= \frac{Estimated\ Benefits}{Discount\ factor}$

$Net\ Present\ Value= (\frac{B_{0}-C_{0}}{(1+i)^{0}})+ (\frac{B_{1}-C_{1}}{(1+i)^{1}})+......+(\frac{B_{5}-C_{5}}{(1+i)^{5}})\\ \Rightarrow NPV= (\frac{B_{0}}{(1+i)^{0}}+\frac{B_{1}}{(1+i)^{1}}+...+\frac{B_{5}}{(1+i)^{5}})-(\frac{C_{0}}{(1+i)^{0}}+\frac{C_{1}}{(1+i)^{1}}+...+\frac{C_{5}}{(1+i)^{5}})\\ \Rightarrow NPV=Total\ Discounted\ Benefits-Total\ Discounted\ Costs\\ \Rightarrow NPV=\$311,172-\$262,517=\$48,655$

Return on Investment (ROI) is a performance measure used to evaluate the efficiency of an investment. To calculate ROI, the benefit (or return) of an investment is divided by the cost of the investment.

$ROI=(\frac{Total Estimated\ Benefits-Total\ Estimated\ Costs}{Total Estimated Costs})*100\\ \Rightarrow ROI=(\frac{400,000-287,500}{287,500})*100=39.13\%$

The Payback Period shows how long it takes for a business to recoup its investment.

Looking at cumulative (Estimated Benefits-Estimated Costs), this parameter turns from (-2,500) in year 3 to (+55,000) in year 4.Therefore, net cash flows turn positive between year 3 & year 4.

Payback occurs in 4th year when net cash flow is positive at 55,000