Question

A firm is planning to purchase a new equipment and answer the following questions according to what you have learned.

Data are shown below:

The new equipment will cost $7,500. And it would be depreciated on a straight-line basis over the project's 5-year life (depreciation rate is 20% per year) and would require additional $200 net operating working capital that would be recovered at the end of the project's life. There is no salvage value.

After purchasing this equipment, firm could sell 1000 products per year at $6 per one. And operating costs is 50% of sale revenue. Tax rate is 40% and Weighted average cost of capital is 15%.

Questions: (Please list the necessary steps not only a final number)

Please show the process of CF estimation and based on the CF information you get to answer following questions.

What is the project's NPV? Should the firm purchase this equipment based on NPV?

What is the project's IRR? Should the firm purchase this equipment based on IRR?

What is the project's MIRR?

What is the project's Payback?

Answer 1

The project details are as given below :

Costs are shown with a negative sign

PV Value of cash flow = CFt / (1+ k) ^ t

where, CFt = Cash flow in year t

k = Cost of capital

t = Year t

For example, PV of 3rd year CF = 2400/ (1+15%)^3 = 1578

NPV = Sum of PV of all cash flows - Initial Cost = 8145 - 7700 = 445

Yes company should purchase the equipment based on NPV as the NPV is positive.

IRR is calculated using the excel function of IRR using 15% as discount rate and all cash flows = 17.39%  

Company should invest based on the IRR as it is higher than the cost of capital / discount rate of 15%

Revenue forecast	0	1	2	3	4	5
Units sold (A)		1000	1000	1000	1000	1000
Sales Price / Unit (B)		6	6	6	6	6
Revenues (C = A x B)		6,000	6,000	6,000	6,000	6,000
Operational Costs D = 50% x C		(3,000)	(3,000)	(3,000)	(3,000)	(3,000)
Depreciation (E = K in Yr 0 /5)		(1,500)	(1,500)	(1,500)	(1,500)	(1,500)
EBIT (F = C + B + E)		1,500	1,500	1,500	1,500	1,500
Taxes @ 40% (G = F x 40%)		(600)	(600)	(600)	(600)	(600)
Net Income (H = F - G)		900	900	900	900	900
Depreciation (E)		1,500	1,500	1,500	1,500	1,500
Net Working Capital Investments (I)	(200)
Return of Net working Capital (J)						200
Capital Expenditure (K)	(7,500)
Free Cash Flow (O = H + E+ I +J +K )	(7,700)	2,400	2,400	2,400	2,400	2,600
Cost of Capital (Discount Rate) R	15.00%
PV Of Free Cash Flow	(7,700)	2,087	1,815	1,578	1,372	1,293
NPV (Sum of PV of all CF)	445
IRR (IRR function in excel)	17.39%

Pay Back Period

Year	Free Cash Flow	Cumulative Cash Flows
0	(7,700)	(7,700)
1	2,400	(5,300)
2	2,400	(2,900)
3	2,400	(500)
4	2,400	1,900
5	2,600	4,500

Since the cumulative value moves from negative to positive in the year 4, the pay back period lies between 3 & 4 years

Pay back period = 3 + 500 (previous yr cumulative Cf) / 2400 (Current years Cash Flow)

= 3.208 years

MIRR = (Sum of FV Positive Cash Flow/ PV of Negative Cash flow)^ (1/n) -1

where, FV = Future value of a cash flow during the life of project

PV = PV of negative cash flow

n = Life of the project

FV is calculated with the formula = Cash flow x (1+ Discount rate)^ t

For example,

For the 2nd year Cash flow of 2400, FV = 2400 x (1+15%)^(5-2) = 2400 x 1.15^3 = 3650

Year	Free Cash Flow	FV of Cash Flow at 15%	PV of Cash Flow
0	(7,700)		(7,700)
1	2,400	4,198
2	2,400	3,650
3	2,400	3,174
4	2,400	2,760
5	2,600	2,600
Sum		16,382	(7,700)
MIRR = (FVCF/ PVCF) ^(1/n) -1 =	16.30%

MIRR = (16382/ 7700)^(1/5) -1 = 16.30%