Question

Managers at Acme Doohickey Co are considering two projects 、 Project A, purchase and operation of a new machine, called the Starpunch, for manufacturing Acme doohickeys. The ife of this project is three years Project &:purchase and operation of a new machine, called the Sunspot, for manufacturing Acme doohickeys. The ife of this project is two years The machines have identical capacity and produce the same doohickey. The company only has floor space in its machinists' shop for one machine. Assure that the appropriate discount rate in 6.3%, compounded annually. Calculate the Equivalent Annual Cash Flow EACF) for Project A Round to the dollar. Do not type the $ symbol. Also, if the EACF is negative, then include a minus sign in your answer Table: Expected Cash Flows for Projects A and B Year revenue A NCF A costs revenue 8 costs B NCF ($23.000) ($29,000) 1$20.000 ($9.000) $20000 ($8.000) $20000 (s8.000) 0 $20,000 ($7,000) 2 $20.000 (S6.000) 3 Note: the table ists net revenue ant net cost for each project and each year. But the table is incomplete; you will to calculate the Net Cash Flows

Answer 1

The effective annual cash flow (EACF) is the annuity amount that would have the same Net present value as the given system of cash flows. So, in order to calculate EACF, we first have to calculate the Net present value of the given cash flows. Then we can calculate the annuity amount that would have the same net present value as calculated.

Step 1 is to calculate the net cash flow, which is simply revenues minus costs in this case. Below table shows the net cash flow amounts:

Next step is to calculate the Net present value of these cash flows. It can be done in excel using the NPV function or by discounting each cash flow using the formula:

$PV=\frac{C}{(1+r)^{n}}$

where,

• C is the cash flow
• r is the discount rate
• n is the time period

Calculations are as shown:

Discount 6.30% rate 4 Project A Project B Costs $29,000 -$9,000 $8,000 $8,000 NCF $29,000 $11,000 $12,000 $12,000 Present values RevenuesCosts Present values $23,000 $12,230 $12,390 5 Year Revenues NCF $29,000 $10,348 $10,620 $9,990 $23,000 -$23,000 $7,000 $13,000 $6,000 $14,000 0 $20,000 $20,000 $20,000 $20,000$ $20,000$ 2 10 NPV, $1,958 NPV, Project B $1,619 Project A

Formulas used in excel:

Discount 6.30% rate Project A Project B Costs $29,000 $9,000 $8,000 $8,000 5 Year Revenues NCF Present values RevenuesCosts NCF Present values 0 $20,000 $20,000 $20,000 -87+C7 |-D7/(1+$C$2pa7 | $20,000 | -$7,000 | -F7+67|-H7/(1+$C$2pa7 10 NPV, NPV, Project B -SUM(16:18) ProjectA SUM(E6:E9)

Next step is to find the value of annuity that has the same NPV value as calculated above with a discount rate of 6.3% and period of 3 years. This is for project A.

This can be done in excel using the PMT function. Implementation is as shown:

Formulas used:

Therefore, EACF for project A is 737 (rounded to the nearest dollar)