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Comparing all methods. Risky Business is looking at a project with the following estimated cash​ flow:...

Comparing all methods. Risky Business is looking at a project with the following estimated cash​ flow: Initial investment at start of​ project: ​$12,300,000 Cash flow at end of year​ one: ​$2,214,000 Cash flow at end of years two through​ six: ​$2,460,000 each year Cash flow at end of years seven through​ nine: ​$2,878,200 each year Cash flow at end of year​ ten: ​$2,214,000 Risky Business wants to know the payback​ period, NPV,​ IRR, MIRR, and PI of this project. The appropriate discount rate for the project is 10​%. If the cutoff period is 6 years for major​ projects, determine whether the management at Risky Business will accept or reject the project under the five different decision models.

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Expert Solution

Risky business
Year Cash flow stream Cumulative cash flow
0 -12300000 -12300000
1 2214000 -10086000
2 2460000 -7626000
3 2460000 -5166000
4 2460000 -2706000
5 2460000 -246000
6 2460000 2214000
7 2878200 5092200
8 2878200 7970400
9 2878200 10848600
10 2214000 13062600
Payback period is the time by which undiscounted cashflow cover the intial investment outlay
this is happening between year 5 and 6
therefore by interpolation payback period = 5 + (0-(-246000))/(2214000-(-246000))
5.1 Years

accept project as payback period is less than cut off period of 6 years

Risky business
Discount rate 10.000%
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream -12300000 2214000 2460000 2460000 2460000 2460000 2460000 2878200 2878200 2878200 2214000
Discounting factor 1.000 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594
Discounted cash flows project -12300000.000 2012727.273 2033057.851 1848234.410 1680213.100 1527466.455 1388605.868 1476971.696 1342701.542 1220637.765 853592.843
NPV = Sum of discounted cash flows
NPV Risky business = 3084208.80
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
accept project as NPV is greater than 0
PI= (NPV+initial inv.)/initial inv.
=(3084208.8+12300000)/12300000
1.25
accept project as PI is greater than 1

IRR

False False Center Center
Risky business
IRR is the rate at which NPV =0
IRR 15.38%
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream -12300000.000 2214000.000 2460000.000 2460000.000 2460000.000 2460000.000 2460000.000 2878200.000 2878200.000 2878200.000 2214000.000
Discounting factor 1.000 1.154 1.331 1.536 1.772 2.045 2.359 2.722 3.141 3.624 4.181
Discounted cash flows project -12300000.000 1918891.839 1847910.213 1601598.838 1388118.762 1203093.841 1042731.234 1057380.078 916439.929 794285.953 529549.313
NPV = Sum of discounted cash flows
NPV Risky business = 0.000
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
IRR= 15.38%

accept project as IRR is greater than discount rate

Combination approach
All negative cash flows are discounted back to the present and all positive cash flows are compounded out
to the end of the project’s life
Thus year 8 modified cash flow=(5220496.19)+(5273228.47)+(4793844.07)+(4358040.06)+(3961854.6)+(3601686)+(3830884.2)+(3482622)+(3166020)+(2214000)
=39902675.59
Thus year 0 modified cash flow=-12300000
=-12300000
Discount rate 10.000%
Year 0 1 2 3 4 5 6 7 8 9 10
Cash flow stream -12300000.000 2214000.000 2460000.000 2460000.000 2460000.000 2460000.000 2460000.000 2878200.000 2878200.000 2878200.000 2214000.000
Discount factor 1.000 1.100 1.210 1.331 1.464 1.611 1.772 1.949 2.144 2.358 2.594
Compound factor 2.594 2.358 2.144 1.949 1.772 1.611 1.464 1.331 1.210 1.100 1.000
Discounted cash flows -12300000.000 0 0 0 0 0 0 0 0 0 0
Compounded cash flows 0.000 5220496.19 5273228.47 4793844.07 4358040.06 3961854.6 3601686 3830884.2 3482622 3166020 2214000
Modified cash flow -12300000.000 0 0 0 0 0 0 0 0 0 39902675.590
Discounting factor (using MIRR) 1.000 1.125 1.265 1.423 1.601 1.801 2.026 2.279 2.564 2.884 3.244
Discounted cash flows -12300000.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 12300000.000
NPV = Sum of discounted cash flows
NPV= 0.00
MIRR is the rate at which NPV = 0 0.00
MIRR= 12.49%
Where
Discounting factor = (1 + discount rate)^(Corresponding period in years)
Discounted Cashflow= Cash flow stream/discounting factor
Compounding factor = (1 + reinvestment rate)^(time of last CF-Corresponding period in years)
Compounded Cashflow= Cash flow stream*compounding factor

MIRR is greater than cost of capital hence accept the project

jeff jeffy answered 1 year ago
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