Question

Heritage Inc. has the option to buy a widget machine. The initial investment required today is $240,000. The machine is expected to generate revenues of $65,000 each year for the next 5 years, at which time it can be sold for $20,000 after-tax. If the firm’s hurdle rate is 15%, what is the NPV? What is the PI? What is the IRR? What is the MIRR? What is the payback period?

Please show all work and formulas. Espically for the IRR and MIRR.

Answer 1

Cost of capital = k	15%
Reinvestment rate = r*	15%
Total years = n	5
Investment = I =	240,000.00

				Terminal Value = TV
Year	Cash flows = CF	Df = 1/(1+k)^Year	Present Value = CF x Df	CF x (1+r*)^(n-Year)
0	-240,000.00	1.000000	-240,000.00	Exclude investment
1	65,000.00	0.869565	56,521.7391	113,685.41
2	65,000.00	0.756144	49,149.3384	98,856.88
3	65,000.00	0.657516	42,738.5551	85,962.50
4	65,000.00	0.571753	37,163.9610	74,750.00
5	85,000.00	0.497177	42,260.0225	85,000.00
		Total PV = NPV =	-12,166.38	458,254.78

NPV =   -12,166.38

PV of Cash Inflows

56,521.74

49,149.3384

42,738.5551

37,163.9610

42,260.0225

Total = 227,833.6161

PI or BC = PV of Cash Inflows / Investment = 227833.6161 / 240000 =	PI or BC =	0.95
MIRR = Modified IRR = (TV ÷ I)1/n – 1 = (458254.78 / 240000)^(1/5)-1 =	MIRR =	13.81%

Payback period and IRR:

		Rate = R =
Year	Cash flows	Cumulative cash flow
0	-$240,000.00	-$240,000.00
1	$65,000.00	-$175,000.00
2	$65,000.00	-$110,000.00
3	$65,000.00	-$45,000.00
4	$65,000.00	$20,000.00
5	$85,000.00	$105,000.00

Payback period = A + |B|/C                                                   

A = Last period with a negative cumulative cash flow                                                 

|B| = Absolute value of cumulative cash flow at end of period A                                            

C = Total cash flow during the period after A                                                  

Payback period = 3+45000/65000                                      

Payback period =    3.69

----------------------------

                                                         

IRR is obtained from trial and error method we have to fix such rate for discount that it forces NPV = 0 or sum of all cash flows equal to zero

IRR = 12.913535208%

		Rate = R =	12.913535208%
Year	Cash flows	Discount factor = Df = 1/(1+R)^Year	Present value = Df x Cash flows
0	-$240,000.00	1.00000	-$240,000.00
1	$65,000.00	0.88563	$57,566.17
2	$65,000.00	0.78435	$50,982.53
3	$65,000.00	0.69464	$45,151.83
4	$65,000.00	0.61520	$39,987.97
5	$85,000.00	0.54484	$46,311.51
		Total of Present Value = NPV=	$0.00