Question

You must analyze a potential new product—a caulking compound that Cory Materials’ R&D people

developed for use in the residential construction industry. Cory’s marketing manager thinks they

can sell 115,000 tube per year at a price of $3.25 per year for 3 years, after which the product will

be obsolete. The required equipment would cost $150,000, plus another $25,000 for shipping and

installation. Current assets would increase by $35,000 while current liabilities would rise by

$15,000. Variable costs would be 60% of sales revenues, fixed costs (excluding depreciation)

would be $70,000 per year, and fixed assets would be depreciated under MACRS with a 3-year life.

The relative depreciation rates would be 33.33%, 44.44%, 14.82% and 7.41%. When production

ceases after 3 years, the equipment will have a market value of $15,000. Cory’s tax rate is 40%

and it uses a 10% wacc for average-risk projects.

a.

Calculate the project’s NPV, IRR, MIRR, PI, payback and discounted payback.

Answer 1

Time line		0	1	2	3
Cost of new machine		-175000
Initial working capital		-20000
=Initial Investment outlay		-195000
3 years MACR rate			33.33%	44.45%	14.81%	7.41%
Unit sales			115000	115000	115000
Profits	=no. of units sold * (sales price - variable cost)		149500	149500	149500
Fixed cost			-70000	-70000	-70000
-Depreciation	=Cost of machine*MACR%		-58327.5	-77787.5	-25917.5	12967.5	=Salvage Value
=Pretax cash flows			21172.5	1712.5	53582.5
-taxes	=(Pretax cash flows)*(1-tax)		12703.5	1027.5	32149.5
+Depreciation			58327.5	77787.5	25917.5
=after tax operating cash flow			71031	78815	58067
reversal of working capital					20000
+Proceeds from sale of equipment after tax	=selling price* ( 1 -tax rate)				9000
+Tax shield on salvage book value	=Salvage value * tax rate				5187
=Terminal year after tax cash flows					34187
Total Cash flow for the period		-195000	71031	78815	92254
Discount factor=	(1+discount rate)^corresponding period	1	1.1	1.21	1.331
Discounted CF=	Cashflow/discount factor	-195000	64573.636	65136.3636	69311.796
NPV=	Sum of discounted CF=	4021.795642

Total Cash flow for the period		-195000	71031	78815	92254
Discount factor=	(1+discount rate)^corresponding period	1	1.111171	1.23470109	1.3719641
Discounted CF=	Cashflow/discount factor	-195000	63924.452	63833.2637	67242.285
NPV=	Sum of discounted CF=	0.000239
IRR is discount rate at which NPV = 0 =	11.12%

MIRR

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 3 modified cash flow=(85947.51)+(86696.5)+(92254)
=264898.01
Thus year 0 modified cash flow=-195000
=-195000

Discount rate	10.000%
Year	0	1	2	3
Cash flow stream	-195000.000	71031.000	78815.000	92254.000
Discount factor	1.000	1.100	1.210	1.331
Compound factor	1.000	1.210	1.100	1.000
Discounted cash flows	-195000.000	0	0	0
Compounded cash flows	0.000	85947.51	86696.5	92254
Modified cash flow	-195000.000	0	0	264898.010
Discounting factor (using MIRR)	1.000	1.108	1.227	1.358
Discounted cash flows	-195000.000	0.000	0.000	195000.000
NPV = Sum of discounted cash flows
NPV=	0.00
MIRR is the rate at which NPV = 0
MIRR=	10.75%
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

PI= (NPV+initial inv.)/initial inv.

=(4021.8+195000)/195000

1.02

Year	Cash flow stream	Cumulative cash flow	Discounting factor	Discounted cash flows project	Cumulative discounted CF
0	-195000	-195000	1	-195000	-195000.00
1	71031	-123969	1.1	64573.63636	-130426.36
2	78815	-45154	1.21	65136.36364	-65290.00
3	92254	47100	1.331	69311.79564	4021.80

Payback period is the time by which undiscounted cashflow cover the intial investment outlay

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-45154))/(47100-(-45154))

2.49 Years

Discounted payback period is the time by which discounted cashflow cover the intial investment outlay

this is happening between year 2 and 3

therefore by interpolation payback period = 2 + (0-(-65290))/(4021.8-(-65290))

2.94 Years

Where

Discounting factor =(1 + discount rate)^(corresponding year)

Discounted Cashflow=Cash flow stream/discounting factor