Question

​Mr Ali has an option of investing in one project from the proposed three different projects. The initial investment and cash flows are given below. (r = 12%)

years

Cf – project 1

Cf – project 2

Cf – project 3

0

(10,000)

(28,000)

(22,000)

1

1000

3000

4000

2

880

7000

1000

3

6000

8000

1000

4

4000

12000

9000

5

2000

7500

11500

6

3650

6400

8900

a. Calculate payback for all three projects​​​​​[1 marks]

b. Calculate discounted payback for all three projects​​​[1 marks]

c. Calculate NPV for all three projects​​​​​[2 marks]

d. Calculate profitability index for all three projects​​​[1 marks]

e. Calculate IRR for all three projects​​​

Answer 1

a. Calculation of Payback Period

Payback Period = E + B / C

where E = Year immediately preceeding to year of recovery

B = Amount Left to be recovered

C = Cash Inflow During the Year of Final Recovery

Year	Cash Flows	Cumulative Cash Flows
Project 1	Project 2	Project 3	Project 1	Project 2	Project 3
1	1,000.00	3,000.00	4,000.00	1,000.00	3,000.00	4,000.00
2	880.00	7,000.00	1,000.00	1,880.00	10,000.00	5,000.00
3	6,000.00	8,000.00	1,000.00	7,880.00	18,000.00	6,000.00
4	4,000.00	12,000.00	9,000.00	11,880.00	30,000.00	15,000.00
5	2,000.00	7,500.00	11,500.00	13,880.00	37,500.00	26,500.00
6	3,650.00	6,400.00	8,900.00	17,530.00	43,900.00	35,400.00

Payback Period

Project 1 = 3 Years + (2120 / 4000) = 3 Years + 0.53 Years = 3.53 Years

Project 2 = 3 Years + (10000 / 12000) = 3 Years + 0.83 Years = 3.83 Years

Project 3 = 4 Years + (7000 / 11500) = 4 Years + 0.61 Years = 4.61 Years

b. Calculation of Discounted Payback Period

Discounted Payback Period = E + B / C

where E = Year immediately preceeding to year of recovery

B = Amount Left to be recovered

C = Discounted Cash Inflow During the Year of Final Recovery

  

Year	Present Value Factor @ 12%	Cash Flows	Discounted Cash Flows	Cumulative Discounted Cash Flows
Project 1	Project 2	Project 3	Project 1	Project 2	Project 3	Project 1	Project 2	Project 3
1	0.8929	1,000.00	3,000.00	4,000.00	892.90	2,678.70	3,571.60	892.90	2,678.70	3,571.60
2	0.7972	880.00	7,000.00	1,000.00	701.54	5,580.40	797.20	1,594.44	8,259.10	4,368.80
3	0.7118	6,000.00	8,000.00	1,000.00	4,270.80	5,694.40	711.80	5,865.24	13,953.50	5,080.60
4	0.6355	4,000.00	12,000.00	9,000.00	2,542.00	7,626.00	5,719.50	8,407.24	21,579.50	10,800.10
5	0.5674	2,000.00	7,500.00	11,500.00	1,134.80	4,255.50	6,525.10	9,542.04	25,835.00	17,325.20
6	0.5066	3,650.00	6,400.00	8,900.00	1,849.09	3,242.24	4,508.74	11,391.13	29,077.24	21,833.94
Total	11,391.13	29,077.24	21,833.94

Discounted Payback Period

Project 1 = 5 Years + (457.96 / 1849.09) = 5 Years + 0.25 Years = 5.25 Years

Project 2 = 5 Years + (2165 / 3242.24) = 5 Years + 0.67 Years = 5.67 Years

Project 3 = More than 6 Years

c. Calculation of NPV

NPV = Discounted Cash Inflows - Initial Cash Outflows

Project -1 = NPV = 11391.13 - 10000 = 1391.13

Project -2 = NPV = 29077.24 - 28000 = 1077.24

Project -1 = NPV = 21833.94 - 22000 = - 166.06

d. Calculation of Profitability Index

PI = Discounted Cash Inflows / Cash Outflow

Project - 1 = PI = 11391.13 / 10000 = 1.14

Project - 2 = PI = 29077.24 / 28000 = 1.04

Project - 1 = PI = 21833.94 / 22000 = 0.99

e. Calculation of IRR

IRR = R_a + [(NPV_a * (R_b - R_a)] / (NPV_a - NPV_b)

Where R_a = Lower Discounting Rate

R_b = Higher Discounting Rate

NPV_a = NPV at R_a

NPV_b = NPV at R_b

Project - 1

Year	Present Value Factor @ 16%	Present Value Factor @ 16.10%	Cash Flows	Discounted Cash Flows @ 16%	Discounted Cash Flows @ 16.10%
1	0.8621	0.8613	1,000.00	862.10	861.30
2	0.7432	0.7419	880.00	654.02	652.87
3	0.6407	0.6390	6,000.00	3,844.20	3,834.00
4	0.5523	0.5504	4,000.00	2,209.20	2,201.60
5	0.4761	0.4741	2,000.00	952.20	948.20
6	0.4104	0.4083	3,650.00	1,497.96	1,490.30
Total	10,019.68	9,988.27

IRR = 16% + (19.68 * 0.10%) / (19.68 - (-11.73)) = 16% + 0.06% = 16.06%

Project - 2

Year	Present Value Factor @ 13%	Present Value Factor @ 13.30%	Cash Flows	Discounted Cash Flows @ 13%	Discounted Cash Flows @ 13.30%
1	0.8850	0.8826	3,000.00	2,655.00	2,647.80
2	0.7831	0.7790	7,000.00	5,481.70	5,453.00
3	0.6931	0.6876	8,000.00	5,544.80	5,500.80
4	0.6133	0.6068	12,000.00	7,359.60	7,281.60
5	0.5428	0.5356	7,500.00	4,071.00	4,017.00
6	0.4803	0.4727	6,400.00	3,073.92	3,025.28
Total	28,186.02	27,925.48

IRR = 13% + (186.02 * 0.30%) / (186.02 - (-74.52)) = 13% + 0.21% = 13.21%

Project - 3

Year

Present Value Factor @ 11.50%

Present Value Factor @ 12%

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