Question

Consider the following 5-years investment table of Agus's cash flow with required return rate j=11% (RRR). Discounted is a discount factor based on RRR. Contribution is amount of money that Agus paid to start the business (investment). Whereas, return is amount of money that Agus received from the investment. Furthermore, PV Contrib is present value of Contribution based on RRR, then Net Cash Flow is Return minus Contribution. Moreover, Discounted Cash Flow is present value of Net Cash Flow based on RRR. Finally, NPV at year "4" is NPV of investment from now (t=0) until year "Y". If t=5 then the investment has settled or matured. Year Discounted Contribution Return PV Contrib Net Cash Flow Discounted Cash Flow NPV at yeart 1 10000 10000 -10000 - 10000 10000 1 0.9009009 3000 3000 2702.7027 0 -10000 2 0.81162243 1000 5000 811.62243 4000 3246.489733 -6753.51027 3 0.73119138 1000 6000 731.19138 5000 3655.956907 -3097.55336 4 0.65873097 1000 6000 658.73097 5000 3293.654871 196.1015102 5 0.59345133 1000 4000 593.45133 3000 1780.353984 1976.455494 Figure 1: Agus's Cash Flow under RRR=11% 0 (a). Calculate the Profitability Index of this investment under required return rate. (b). Find the discounted payback period over this investment under required return rate. (c). From the cash flow of contribution and return, Agus knew that this investment will yield an internal return rate (IRR = 0.172894062). Based on modified internal return rate (MIRR), what can you conclude from Agus's investment? Please give a comment to analyze this investment. Show your work to produce the equated value of modified NPV under MIRR method. Hint: You have to look for theory of Profitability Index, Discounted Payback Period, and MIRR. For Profitability Index (PI) = NPV/I and it's computed under RRR (1). For Discounted Payback Period, find the minimum k for which NPV until k-year is positive under RRR (). For MIRR method, you must show that present value of Return under IRR is greater than the present value of Contribution under RRR. State your comment and conclusion from your work especially in MIRR.

Answer 1

As per the question, we have below :

Required rate of return(RRR) = 11%

Time(t) = 5 years

(a) The investment made by Agus will have Profitability Index(PI) = Present Value of future cash flows/Initial Investment

where, Initial Investment = 10,000

  Present value of cash flows for 5 years =  

Years	PV of Cash Flows
2	3246.489733
3	3655.956907
4	3293.654871
5	1780.353984
Total	11,976.455495

Therefore, PI = 11,976.455495/10,000

= 1.1976455495

(b) Discounted Payback Period is calculated below :

Year	Discounted Cash Flows	Cumulative Discounted Cash Flows
0	-10000	-10000
1	0	-10000
2	3246.489733	-6753.510267
3	3655.956907	-3097.55336
4	3293.654871	196.101511
5	1780.353984	1976.455494

Therefore, discounted payback period = 3+{(-3097.55336)/3293.654871}

= 2.0595 years