Question

Calculate the Net Present Value and Pay-Back Period for the below Investment (please show calculations):

Rate of Return: 15%

Inflation Rate: 2%

Year	Investment Cost	Recurring Cost	Savings	Residual Value
1	$           6,500,000
1		$           300,000	$ 1,300,000
2		$           200,000	$ 2,000,000
3		$           125,000	$ 3,500,000
4		$           125,000	$ 4,000,000
5		$           125,000	$ 5,000,000	$                      3,500,000

Please note: all investment costs will be assumed to occur at the beginning of the year and all recurring costs and revenues at the end of the year

Answer 1

Real interest rate = Nominal interest rate – Inflation

                                = 15 % - 2 % = 13 %

Computation of annual cash inflow:

Year	1	2	3	4	5
Saving	$1,300,000	$2,000,000	$3,500,000	$4,000,000	$5,000,000
Less: Recurring cost	$300,000	$200,000	$125,000	$125,000	$125,000
Add: Residual value	-	-	-	-	$3,500,000
Annual cash inflow	$1,000,000	$1,800,000	$3,375,000	$3,875,000	$8,375,000

Computation of NPV:

Year	Cash flow (C)	PV Factor computation	PV Factor @ 13 % (F)	PV (= C x F)
1	($6,500,000)	1/(1+0.13)^0	1	($6,500,000.0000)
1	$1,000,000	1/(1+0.13)^1	0.884955752212	$884,955.7522
2	$1,800,000	1/(1+0.13)^2	0.783146683374	$1,409,664.0301
3	$3,375,000	1/(1+0.13)^3	0.693050162278	$2,339,044.2977
4	$3,875,000	1/(1+0.13)^4	0.613318727679	$2,376,610.0698
5	$8,375,000	1/(1+0.13)^5	0.542759935999	$4,545,614.4640
			NPV	$5,055,888.6137

NPV of the investment is $ 5,055,888.61

Computation of discounted payback period:

Year	Cash flow	PV Factor computation	PV Factor @ 13 % (F)	Discounted cash flow	Discounted ‘CUM cash flow
1	($6,500,000)	1/(1+0.13)^0	1	($6,500,000.0000)	($6,500,000.0000)
1	$1,000,000	1/(1+0.13)^1	0.884955752212	$884,955.7522	($5,615,044.2478)
2	$1,800,000	1/(1+0.13)^2	0.783146683374	$1,409,664.0301	($4,205,380.2177)
3	$3,375,000	1/(1+0.13)^3	0.693050162278	$2,339,044.2977	($1,866,335.9200)
4	$3,875,000	1/(1+0.13)^4	0.613318727679	$2,376,610.0698	$510,274.1497
5	$8,375,000	1/(1+0.13)^5	0.542759935999	$4,545,614.4640	$5,055,888.6137

Discounted Payback Period = A + B/C

Where,

A = Last period with a negative discounted cumulative cash flow = 3

B = Absolute value of discounted cumulative cash flow at the end of the period A = $ 1,866,335.92

C = Total discounted cash flow during the period after A = $ 2,376,610.0698

Payback Period = 3 +│$ (1,866,335.92) │/$ 2,376,610.0698

                             = 3 + $ 1,866,335.92/$ 2,376,610.0698

                             = 3 + 0.78529328129 = 3.78529328129 or 3.79 years

Discounted Payback period of the project is 3.79 years

*****Discounted payback period has been computed as rate of interest is given.