Question

5) Anderson Equipment Manufacturing produces equipment for the natural gas industry. The company management is considering purchasing new controllers for the fabricating machines. The new controllers are expected to increase efficiency and product quality. The engineering staff estimate that annual net cash savings from increased efficiency will be $35,000 per year for four years. The existing controllers can be sold for $8,000. The new controllers have a purchase price of $75,000 and will require installation costs in the amount of $4,500. The annual software contract for the new controllers is $1,700; the controllers will be depreciated using the straight-line method. The salvage value of the new controllers at the end of four years is estimated to be $10,000. The company has a required rate of return of 15%.

Required:

1. Determine the net present value of the investment in the new controllers.
2. Estimate the internal rate of return (within a 5% range) of the investment in the new controllers.

Answer 1

a) Calculation of Present Value of the Investment (Amounts in $)

Cash Flows	Amounts (1)	Relevant Present Value Factor (2)	Present Value (1*2)
Annual cash savings	35,000	2.85498 [PVAF(15%, 4 yrs)]	99,924
Sale price of existing controller	8,000	1	8,000
Purchase price of controller	(75,000)	1	(75,000)
Installation cost	(4,500)	1	(4,500)
Annual Software Expense	(1,700)	2.85498 [PVAF(15%, 4 yrs)]	(4,853)
Salvage Value at the end of 4 years	10,000	0.57175 [PVF(15%, 4 yrs)]	5,718
Net Present Value			29,289

Therefore the net present value of the investment in the new controllers is $29,289.

Working Notes:-

1) PVAF denotes present value annuity factor and PVF denotes present value factor. The interest rate to be used for discounting is 15% and number of periods is 4 years.

b) Internal rate of return is the interest rate at which net present value of cash flows is zero.

For calculating IRR, we need to assume two interest rates (one is lower and another is higher interest rate).

Let lower interest rate is 15% and higher interest rate is 20%. The net present value at 15% is calculated in part 1 and net present value at 20% is calculated as follows:-

Calculation of Present Value of the Investment at 20% (Amounts in $)

Cash Flows	Amounts (1)	Relevant Present Value Factor (2)	Present Value (1*2)
Annual cash savings	35,000	2.58873 [PVAF(20%, 4 yrs)]	90,606
Sale price of existing controller	8,000	1	8,000
Purchase price of controller	(75,000)	1	(75,000)
Installation cost	(4,500)	1	(4,500)
Annual Software Expense	(1,700)	2.58873 [PVAF(20%, 4 yrs)]	(4,401)
Salvage Value at the end of 4 years	10,000	0.48225 [PVF(20%, 4 yrs)]	4,822
Net Present Value (NPV)			19,527

IRR = R1+{[NPV1*(R2-R1)]/(NPV1 - NPV2)}

Where, R1 = Lower interest rate = 15%

R2 = Higher interest rate = 20%

NPV1 = NPV at R1 = $29,289

NPV2 = NPV at R2 = $19,527

IRR = 15% + {[29,289*(20%-15%)]/(29,289-19,527)}

= 0.15 + [(29,289*5%)/9,762]

= 0.15 + (1,464/9,762)

= 0.15 + 0.15 = 0.30 or 30%

Therefore Internal rate of return will be around 30% approximately.