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You are considering a new product launch. The project will cost $680,000, have a four-year life,...

You are considering a new product launch. The project will cost $680,000, have a four-year life, and have no salvage value; depreciation is straight-line to zero. Sales are projected at 100 units per year, price per unit will be $19,000, variable cost per unit will be $14,000, and fixed costs will be $150,000 per year. The required return on the project is 15%, and the relevant tax rate is 35%. Ignore the half-year rule for accounting for depreciation.

a. Calculate the following six numbers for this project. Round your answers to two decimal places.

(i) NPV

(ii) Profitability Index (PI)

(iii) Payback period (in years)

(iv) Discounted payback period (in years)

(v) Internal Rate of Return (IRR in %)

(vi) Average Accounting Return (AAR in %)

Hint: Net Income = {[(Price – variable cost)*Quantity Sold] – Fixed Costs – Depreciation} * (1 – Tax rate)

Solutions

Expert Solution

Solution:-

Calculation of Net Income
Particulars Amount (In $'s)
Selling price per unit………………(a)                  19,000
Less: Variable Cost per Unit………..(b)                  14,000
Contribution per unit ………….(a)-(b)                    5,000
Units Sold per year…………………('c)                       100
Contribution …………...………….[(a)-(b)]*('c)               500,000
Less: Fixed Cost…..               150,000
Earnings before Depreciation               350,000
Less: Depreciation               170,000
Earnings before Tax               180,000
Less: Tax @35%                  63,000
Earnings after Tax               117,000
Add: Depreciation               170,000
Cash flow per year               287,000

1. Calculation of Net Present Value

Formula

Net Present Value = Present value of Cash Inflows - Initial Investments

Year Cash flow Present Value factor @15% Present Vale Working of Present Value
1     287,000 0.8696    249,565.22 1/1.15^1
2     287,000 0.7561    217,013.23 1/1.15^2
3     287,000 0.6575    188,707.16 1/1.15^3
4     287,000 0.5718    164,093.18 1/1.15^4
Present Value of Cash Inflows    819,378.79
Less: Cash Outflow    680,000.00
Net Present Value    139,378.79

2. Profitability Index (PI)

Formula

Profitability Index = Present value of Cash Inflow / Initial Outflow

Profitability Index = 819,378.79 / 680,000

Profitability Index = 1.205

3. Payback Period

Year Cash Inflows Cummulative Cash Inflows
1           287,000                                   287,000
2           287,000                                   574,000
3           287,000                                   861,000
4           287,000                                1,148,000

Initial Investment = $ 680,000

Payback Period = 2 Years + (680,000 -574,000) / (861,000-574,000)

Payback Period = 2 Years + 106,000 / 287,000

Payback Period = 2 Years + 0.37 = 2.37 Years

4.Discounted Payback Period

Year Cash flow Present Value factor @15% Present Vale Cummulative Present Value
1     287,000 0.8696    249,565.22                                  249,565.22
2     287,000 0.7561    217,013.23                                  466,578.45
3     287,000 0.6575    188,707.16                                  655,285.61
4     287,000 0.5718    164,093.18                                  819,378.79

Initial Investment = $ 680,000

Discounted Payback Period = 3 Years + (680,000 -655,285.61) / (819,378.79-655,285.61)

Discounted Payback Period = 3 Years + 24714.39 / 164093.18

Discounted Payback Period = 3 Years + 0.15 = 3.15 Years

5. Internal Rate of Return

Cash Outflow = Cash Inflow

$ 680,000 = 287,000 / (1+R)^1 + 287,000 / (1+R)^2 + 287,000 / (1+R)^3 + 287,000 / (1+R)^4

Let R = 10%

Year Cash flow Present Value factor @10% Present Vale
1     287,000 0.9091      260,909.09
2     287,000 0.8264      237,190.08
3     287,000 0.7513      215,627.35
4     287,000 0.6830      196,024.86
Present Value of Cash Inflows      909,751.38

Let R = 30%

Year Cash flow Present Value factor @30% Present Vale
1     287,000 0.7692      220,769.23
2     287,000 0.5917      169,822.49
3     287,000 0.4552      130,632.68
4     287,000 0.3501      100,486.68
Present Value of Cash Inflows      621,711.07

Therefore ,

10% --------------------------------- $ 909,751.38

R-------------------------------------- $ 680,000

30%-----------------------------------$621,711.07

R - 30% / 30%-10% = 680,000-621,711.07 / 621,711.07 -909,751.38

R - 30% / 20% = 58288.93 / - 288,040.31

R- 30% = 20 % * (-0.2024)

R = 30% - 4.048%

R = 25.952%

Internal Rate of Return = 25.952%

6. Average Accounting Rate of Return

Accounting Rate of Return = (Earing after Tax / Initial Investment) *100

Accounting Rate of Retrun = (117,000 / 680,000)*100

Accounting Rate of Return = 17.21%


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