Question

A waste disposal company is considering the replacement of one of its aging trucks. The key parameters of the three trucks under scrutiny are provided below.
Parameters	Delta	Epsilon	Zeta
1. Initial Cost ($)	250,000	375,000	450,000
2. Revenues ($)	230,000 at EOY1 increasing by 2.5% annually thereafter	195,000 at EOY1 increasing by 3,000 annually thereafter	235,000 at EOY1 decreasing by 1% annually thereafter
3. Operating costs ($)	140,000 at EOY1 decreasing by 2,000 annually thereafter	125,000 at EOY1 decreasing by 2% annually thereafter	EOY1-EOY4 = 125,000; EOY5-EOY8 = 135,000 EOY9-EOY12 = 170,000 EOY13-EOY16 = 190,000
4. End-of-life salvage value ($)	-20,000	7,000	-20,000
5. Useful life (years)	4	8	16
EOY = End-of-year Industry Standard = 4 years MARR = 10%

1. 25. The incremental External Rate of Return (ΔERR) between the Epsilon and Zeta trucks (first decimal; no rounding) is

a) 10.4%; b) 10.6%; c) 10.8%; d) 11.3%.

1. 26. From your calculations, the best truck based on the external rate of return (ERR) method is
      a) Delta; b) Epsilon; c) Zeta.

1. 27. If the company’s truck budget is $850,000, which truck(s) should it purchase assuming that trucks are independent investments?
      a) Zeta only; b) Delta and Epsilon; c) Delta and Zeta; d) Epsilon and Zeta.

1. 28. Donald plans to make $200 bank deposits at the end of every other month in 2019 (i.e., end of February, end of April, end of June … end of December).

What is the equivalent monthly (end of each month of12 months) deposit if the interest rate is 12% compounded monthly?

a) 200(A/F,12%/12,2)
b) 200/2
c) 200(A/P,12%/12,2)
d) 200(6)(A/F,12%,12)

Hint: Delta's NFW = $81,900

Epsilon's NPW = $89,000

Zeta's NFW = $709,100

Answer 1

Payback period is the time (usually in years) required by a project to recover the invested money.

Formula = Total Investment ÷ (Net) Annual Cash Inflows

Calculating Cash Infow for the following:

Cash Inflows less Cash Outflows = Revenues less Operating Costs

Note: Salvage value is after the operating period, hence ignored.

Delta : 230,000 increasing at 2.5% for 4 years is 253,877

less

140,000 reduced by 2000 each year for 4 years is 134,000

equals 119,877

Eplison: 195,000 increasing at 3,000 each year for 8 years is 207,000

less

125,000 decreasing at 2% for 8 years is 108,515

equals 11,362

Zeta: 235,000 decreasing at 1% for 16 years is 200,093

less

Average of 4 years 155,000

equals 45,093

Payback Period for

Delta = 250,000 ÷ 119,877 = 2.08 years

Eplison = 375,000 ÷ 11,362 = 33 years

Zeta = 450,000 ÷ 45,093 = 9.97 years

Best truck is Delta.

BCR or Benefit to Cost Ratio gives an idea about the feasibility of a project.

BCR of Delta = NPV of Benefits ÷ Net of Investment including salvage value

= 253,877 ÷ (250,000 + (-20,000))

= 1.10 Option (d)

BCR of Zeta = 200,093 ÷ 430,000 = 0.46 None of the above

Incremental BC Ratio = .75 (Sum of Benefits divided by Initial Costs plus Salvage Vales)

The incremental internal rate of return is the IRR of the incremental cashflows of the two projects.

Incremental cash flow is the difference between the cash flows of the two projects over the lifetime.

For evaluation we need to consider both projects for equal useful lives of 10 years.

Hence at the end of the fifth year of the Alpha project the initial cost will again be incurred and the project will replace for another five years period.

IRR is the interest rate at which the NPW is zero.

PW = Cashflow / ((1 + MARR) ^ number of periods)

NPW = Sum of the present worths of all the cashflows

IRR is calculated through trial and error basis it is placed in the PW and NPW formulae and tried till NPW becomes zero.

Through trial and error the incremental IRR between Alpha and Gamma comes to 5.41%

so) 25. c

26. d

27 a

28 c