Question

Company BW has the following two investment opportunities (A and B). Which project is better, according to MIRR? Which project is better, according to Discounted Payback period? Net Cash Flows End of Year 0 1 2 3 Project A -4,000 1,500 3,000 2,500 Project B -5,500 3,500 2,800 1,900

discount rate 9%

Answer 1

Given Information
Years	Project A	Project B
0	-4000	-5500
1	1500	3500
2	3000	2800
3	2500	1900
Discounting Rate	9%

Years	Project A	Project B	Present Value @ 9%	Project A Discounted Cash flows	Project B Discounted Cash flows
0	-4000	-5500	1.0000	-4000.00	-5500.00
1	1500	3500	0.9174	1376.15	3211.01
2	3000	2800	0.8417	2525.04	2356.70
3	2500	1900	0.7722	1930.46	1467.15

Modified Internal Rate of Return (MIRR) Calculation

Where n is the Number of Years of the project

Years (a)	Project A (b)	Project B (c)	Years to be compounded (d)	Compounding Rate @ 9% for n Years (e)	Compounded Cashfows of Project A (f=b*e)	Compounded Cashfows of Project B (g=c*e)
1	1500	3500	2	1.1881	1782.15	4158.35
2	3000	2800	1	1.0900	3270	3052
3	2500	1900	0	1.0000	2500	1900
Total Compounded Cashflows (i)	7552.15	9110.35
Initial Cashflows (ii)	4000	5500
(iii) = (i)/(ii)	1.8880375	1.656427273
(iv) = (iii)^1/3	1.235957504	1.183198083
MIRR = (iv) - 1	0.235957504	0.183198083
MIRR in Percentage	23.60%	18.32%

Discounted Payback Period Calculation

Years	Project A Discounted Cashflows	Cumulative Cashflows	Proportionate Years to become positive
0	-4000.00	-4000.00
1	1376.15	-2623.85	Payback Period Not reached
2	2525.04	-98.81	Payback Period Not reached
3	1930.46	1831.65	2.05	<See Note

Note: Cumulative cash flows became positive in year 3. Therefore, Discounted payback period lies between year 2 and Year 3. 98.81 cash flows are to be recovered in year 3 but 1930.46 cash inflows occurred in year 3 which mean that 98.81/1930.46 = 0.05 years is the time taken to recover 98.81 cash flows. Therefore, the total discounted Payback period of Project A is 2+0.05 = 2.05 Years

Years	Project B Discounted Cashflows	Cumulative Cashflows	Proportionate Years to become positive
0	-5500.00	-5500.00
1	3211.01	-2288.99	Payback Period Not reached
2	2356.70	67.71	1.97	<See Note
3	1467.15	1534.86

Note: Cumulative cash flows became positive in year 2. Therefore, Discounted payback period lies between year 1 and Year 2. 2288.99 cash flows are to be recovered in year 2 but 2356.7 cash inflows occurred in year 2 which mean that 2288.99/2356.7 = 0.97 years is the time taken to recover 2288.99 cash flows. Therefore, total discounted Payback period of Project A is 1+0.97 = 1.97 Years

Project Selection

Method	Project A	Project B	Project Selection Rule	Project Selected
MIRR	23.60%	18.32%	Select Highest MIRR	Project A
Discounted Payback Period	2.05	1.97	Select Lowest Discounted Payback period	Project B

Please give me a like if you find this answer helpful! Let me know if you have any doubts in the comments section. Happy to help!