In: Finance
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)
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%