Question

Lou Barlow, a divisional manager for Sage Company, has an opportunity to manufacture and sell one of two new products for a five- year period. His annual pay raises are determined by his division's return on investment (ROI), which has exceeded 19% each of the last three years. He has computed the cost and revenue estimates for each product as follows: Product A Product B $ 190,000 $ 400,000 Initial investment: Cost of equipment (zero salvage value) Annual revenues and costs: Sales revenues Variable expenses Depreciation expense Fixed out-of-pocket operating costs $ 270,000 $ 128,000 $ 38,000 $ 72,000 $ 370,000 $ 178,000 $ 80,000 $ 52,000 The company's discount rate is 17%. Click here to view Exhibit 13B-1 and Exhibit 13B-2, to determine the appropriate discount factor using tables. Required: 1. Calculate the payback period for each product. 2. Calculate the net present value for each product. 3. Calculate the internal rate of return for each product. 4. Calculate the project profitability index for each product. 5. Calculate the simple rate of return for each product. 6a. For each measure, identify whether Product A or Product B is preferred. 6b. Based on the simple rate of return, Lou Barlow would likely:

Answer 1

You have posted 6 sub parts and I am answering for the first 4 sub parts. If you want answers for the other parts post the question with unanswered parts.

1. Calculation of Payback period for each project:

For Product A, Initial investment is $ 190,000

Formula for Payback period =

Initialinvestment Annualcashin flow

Payback period   =

190,000 70,000

= 2.714 years

For Product B, initial investment is $ 400,000

Payback period =

400,000 140,000

= 2.86 years

Working note:

Calculation of Initial Cash inflow,

Particulars	Product A	Product B
Sales	270,000	370,000
Less:
Variable cost	(128,000)	(178,000)
Depreciation	(38,000)	(80,000)
Fixed Operating cost	(72000)	(52000)
Net Income	32,000	60,000
Add:
Depreciation	38000	80000
Net Cash Inflow	70000	140000

2. Calculation of Net Present value for each Product

For product A,

Initial investment = $ 190,000

Annual cash inflow = $ 70,000

Discounting rate @17% for 5 years = 3.199 or 3.20

Present value of Cash inflow = 70,000* 3.20

= $ 224,000

Net present value = Pv of Cash inflows - Pv of Cash outflows

= 224,000 - 190,000

= $ 34,000

For Product B,

Initial Investment = $ 400,000

Annual cash inflow = $ 140,000

Discounting rate at 17% for 5 years = 3.20

Present value of cash inflows = 140,000 * 3.20

= $ 448,000

Net Present value = 448,000 - 400,000

= $ 48,000

3. Calculation of internal rate of return for each product

Internal rate of return is defined at 2 present value factors where Npv is zero.

We have given discounting factor at 17% (lower discount rate) and I assume 2nd factor as 19%(higher discount rate) .

For product A

Cash inflow = $ 70,000

Discounting factor at 19% for 5 years = 3.05

Present value of cash inflows = Cash inflow * 3.05

= 70,000 * 3.05

= $ 213,500

Present value of Cash outflow = 190,000

NPV for Product A @19% = 213,500 - 190,000

= $ 23,500

NPV for Product A @ 17% = 34,000

Formula for calculating Internal rate of return

^{=$\large r_a{}$+}
_{NPV NPV, - NPV.}

^ro-ra)

^{where,  $\large r_{a}$ = lower discount rate @ 17%}

^{$\large r_{b}$ = higher discount rate @ 19%}

   
^{NPVA
= NPV at $\large r_{a}$}

  
NPV)
= NPV at $\large r_{b}$

Hence, IRR = 17% +

34000 23500 -34000(19-17)

= 17 +
_{| 34000 -10500 -}

  = 17 + 3.24(2)

= 17 + 6.48

= 23.48%

At 23.48% Npv will be zero.

For Product B,

Cash inflow = $ 140,000

Discounting factor at 19% for 5 years = 3.05

Present value of cash inflows = 140,000 * 3.05

= $ 427,000

Present value of cash outflow = $ 400,000

NPV @19% = 427,000- 400,000

= $ 27,000

NPV @ 17% = $ 48000

IRR for Product B,

= 17% +

48000 27000-48000(19-17)

= 17 +

| 48000 -21000 (19-17)

= 17 - 2.29(2)

= 17 - 4.58

= 12.42

4. Calculation of Probability Index for two products

Probability Index =

Presentvalueof cashflows Initialinvestment

For Product A,

Present value of Cash inflows = 224,000

Cash outflow = 190,000

Probability index =

224,000 190,000

= 1.18

For Product B,

Present value of cash inflows = $ 448,000

Cash outflow = 400,000

Probability index =

448,000 400,000

= 1.12