Solving for Unknowns Follow the format shown in Exhibit 14B-1 and Exhibit 14B-2

Question

Solving for Unknowns

Follow the format shown in Exhibit 14B-1 and Exhibit 14B-2 as you complete the requirements below. Each of the following scenarios are independent. Assume that all cash flows are after-tax cash flows. Thomas Company is investing $120,000 in a project that will yield a uniform series of cash inflows over the next four years. Video Repair has decided to invest in some new electronic equipment. The equipment will have a three-year life and will produce a uniform series of cash savings. The NPV of the equipment is $1,750, using a discount rate of 8 percent. The IRR is 12 percent. A new lathe costing $60,096 will produce savings of $12,000 per year. The NPV of a project is $3,927. The project has a life of four years and produces the following cash flows: The cost of the project is two times the cash flow produced in Year 4. The discount rate 10 percent. If the internal rate of return is 14 percent for Thomas Company, how much cash inflow per year can be expected? If required, round to the nearest dollar. $ Determine the investment and the amount of cash savings realized each year for Video Repair. If required, round to the nearest dollar. Savings each year $ Original investment $ For Scenario c, how many years must the lathe last if an IRR of 18 percent is realized? Round your answer to the nearest year. years For Scenario d, find the cost of the project and the cash flow for Year 4. Round present value calculations and final answers to the nearest dollar. Cost of the project $ Cash flow for year 4 $

Explanation / Answer

a) If Company has IRR of 14 %,
Then total cash flow of project over 4 years can be calculated as = Cost of project x 140 %,

where 140 % represents IRR factor (14 % equivalent to 140 % cash inflow) for cash inflows

So 120000 x 140 %, = 168000 is total cash inflow of project

Annual cash inflow = Total cash inflow / no. of years of project

= 168000 / 4, =$42000

b)

c) calculating manually annuity factor at 18 % for 14 years i.e. 5.01

we observe that 12000 saving annualy at annuity factor of 5.01 produces discounted cash inflows at 60096.74

So number of years lathe must last is 14 years

d) For project d we are given 10% discount factor is applicable .

time period of project = 4 years

disounting factors as year 1 = 0.909

year 2 =0.826

year 3 = 0.751

year4 = 0.683

We are given cash inflow for 1st - 3 years which are discounted as follows

Accumulated discounted value at end of three years = 9091 +9917 +11270, = 30278

We will assume cash infloe for 4 th year as 'x' , as we are not provided with the same

also it has been provided cost of project is 2 times inflow at year 4, so cost of project can be stated as '2x'

discounted value at year 4 will be = inflow at year 4 x 0.683 ( discount factor), = 'x' x 0.683, =0.683 x

Now We are given NPV as 3927

which can be calculated by deducting present value of cah inflows from present value of cash outflows

We can summarise this equation as

2x - ( 30278 + 0.683x) = 3927

Where 2x is cost of project

( 30278 + 0.683x) = present value of cash inflows

3927 as NPV

Solving equation

2x – 30278 – 0.683x = 3927

1.317x = 3927 + 30278

1.317 x =34205

x = 34205 / 1.317

x = 25971.91

or x = 25972 ( cash flow at year 4)

cost of project = 2 x 25972,= 51944

Year Cash inflow Discount factor discounted value 1 10000 0.909 9091 2 12000 0.826 9917 3 15000 0.751 11270

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