Question

1- What is the present value of a stream of income resulting from an initial investment of $2000 (with an interest rate of 7%) with net cash flows of $100 after one year, $200 after two years, $300 after the third and fourth years, $600 after the fifth and sixth years and $550 after the seventh and eighth years?

2- What is the internal rate of return of the stream of rents from the previous question?

3- What is the payback period of the stream of rents from Question 1?

4- Calculate the Accounting Rate of Return (ARR) for question 1. [Note, sometimes this is referred to as the Average Accounting Return, or AAR]. We assume that there is no salvage value for this investment after eight years (this investment has a useful life of eight years).

5- What is the profitabilty index for the asset in Question 1?

Answer 1

1. Calculation of Net Present value

Year	Cashflow	PVF	PV
1	100	0.9346	93.45794
2	200	0.8734	174.6877
3	300	0.8163	244.8894
4	300	0.7629	228.8686
5	600	0.7130	427.7917
6	600	0.6663	399.8053
7	550	0.6227	342.5124
8	550	0.5820	320.105
		PVIF	2232.118
		PVOF	2000
		NPV	232.118

2. Calculation Of IRR

Year	Cashflow	PVF @10 %	PV	PVF @9 %	PV
1	100	0.9091	90.90909	0.9174	91.7431
2	200	0.8264	165.2893	0.8417	168.3360
3	300	0.7513	225.3944	0.7722	231.6550
4	300	0.6830	204.904	0.7084	212.5276
5	600	0.6209	372.5528	0.6499	389.9588
6	600	0.5645	338.6844	0.5963	357.7604
7	550	0.5132	282.237	0.5470	300.8688
8	550	0.4665	256.5791	0.5019	276.0265
		PVIF	1936.55		2028.876

IRR is between 9% & 10 % . Using interpolation exact IRR will be

IRR = LR + PVIF(LR) - PVOF / PVIF (LR) - PVIF(HR)

= 9 + (2028.87- 2000)/(2028.87 - 1936.55)

= 9.31%

3. Calculation Of Pay Back Period

Year	Cashflow	Cumulative CF
1	100	100
2	200	300
3	300	600
4	300	900
5	600	1500
6	600	2100
7	550	2650
8	550	3200

PBP is between 5 and 6 year. Using interpolation exact PBP will be

IRR = LY + Cumulative CF(HY) - Investment / Cumulative CF (HY) - Cumulative CF(LY)

= 5 + (2100- 2000)/(2100 - 1500)

= 5.1667 Years

4. ARR = Average PAT / Average Investment * 100

=150/1000*100 = 15%

Average PAT = (Total CFAT - Total Depreciation ) / Life = (3200 - 2000) / 8 = 150

Average Investment = (Initial cost + Salvage) / 2 = (2000+0)/ 2 = 1000

5. Profitability Index = PVIF / PVOF= 2232.118/2000 = 1.116