Question

1. SpinCo. is considering a new investment in a 3 year project to manufacture and sell turntables. The firm believes it can sell turntables for $900 each and manufacture them at a variable cost per unit of $400 excluding depreciation expense. The estimated annual SG&A costs for the project are $1 million excluding depreciation expense. The project will require an upfront investment in new fixed assets of $6 million. SpinCo. will depreciate these assets on a straight line basis over the 3 year life of the project. SpinCo. expects to sell the fixed assets at the termination of the project for a salvage value of $1 million. The project is expected to require operating capital investments of $500k per year in years 1, 2 and 3. SpinCo. expects to recapture all of its operating capital investment at the termination of the project. SpinCo. has a 30% tax rate and requires a return of 12.19% on any new investments. The firm believes it can sell 10,000 turntables per year. (20 points)

1. What is the proposed project's Net Present Value?

2. What is the proposed project’s Profitability Index? (2 decimal places)

3. Is the project’s IRR greater than or less than 12.19% (please circle or highlight your answer)

Answer 1

Solution:

1.Calculation of NPV, Profitability Index

SL NO		Year	1	2	3
A		Sales units	10,000	10,000	10,000
B		rate per unit	900	900	900
C=A*B		Sales ($)	9,000,000	9,000,000	9,000,000
D	Less	Variable cost ($)	4,000,000	4,000,000	4,000,000
E	Less	SGA cost ($)	1,000,000	1,000,000	1,000,000
F	Less	Depreciation ($)	1,666,667	1,666,667	1,666,667
G	Less	operating capital investment ($)	500,000	500,000	500,000
H		PBT ($)	1,833,333	1,833,333	1,833,333
I=H*30%		tax@30%	5,50,000	5,50,000	5,50,000
J=H-I		PAT ($)	1,283,333	1,283,333	1,283,333
K	Add	Depreciation ($)	1,666,667	1,666,667	1,666,667
L		PATBD(Cashflows) ($)	2,950,000	2,950,000	2,950,000
	Add	Salvage Value at 3rd year plus operating capital investment ($)			2,500,000
		Total Cashflow	2,950,000	2,950,000	54,50,000
M		[email protected]%	0.89134504	0.79449598	0.708170051
N		PV ($)	2629467.86	2343763.14	3859526.77
O		Total PV of cash inflow ($)			8832757.78
P		Initial investment (Year 0) in ($)			6,000,000
Q=O-P		NPV ($)			2832757.78
R=0/P		Profitability index			1.47

2.Calculation of IRR:

Using Interpolation we find 35% and 40% as rate:

IRR=

LR+(IV@LR-MV/IV@LR-IV@HR)*(HR-LR)

= 35+(6018950-6000000)/(6018950-5598396)

=35.225%

Explanation:

PVAF, 35%,3years = 6018950 (IV at LR)

PVAF, 40%,3Years= 5598396 ( IV at HR)

Initial Value= 6000000 (MV)

Hence, project IRR is greater than 12.19%.

Working Note on IRR

Year	1	2	3	Cashflows
Cashflows	2950000	2950000	5450000	11350000
PVF 12.19%	0.891345	0.794496	0.70817
PV @ 12.19%	2629468	2343763	3859527	8832757.78
PVF 35%	0.740741	0.548697	0.406442
PVF 40%	0.714286	0.510204	0.364431
PV at 35%	2185185	1618656	2215109	6018950.363
PV @ 40%	2107143	1505102	1986152	5598396.501

Notes:
PV	present value
PBT	profit before tax
PAT	profit after tax
PBTAD	profit before tax after depreciation
IRR	internal rate of return
NPV	net present value
PI	profitability Index

*Internal rate of return formula:

LR+(IV@LR-MV/IV@LR-IV@HR)*(HR-LR)
where,
LR	lower rate
HR	higher rate
IV@LR	initial value at lower rate
IV@HR	initial value at higher rate
MV	Net present value/market value