The following annual cash flows [$85, $160, $230, $285, $255] are the basis for

Question

The following annual cash flows [$85, $160, $230, $285, $255] are the basis for the following questions:

A) If the interest rate on deposits is 5.5% and the payment day 1 is $85 instead of after one year, what is the future value of the account at the end of five years?

B) If the hurdle rate is 5.5% what is the PV of these cash flows?

C) If it cost $950 to buy this cash flow would you invest?

D) What is the internal rate of return on this cash flow if the first and second amounts are negative and $85 first payment is paid out immediately?

E) If this is the cash flow is from an investment in a piece of machinery costing $600 what is the payback period?

Explanation / Answer

Part a)

Since, the payment day is today, the future value for 1st year cash flow would be calculated for 5 years and so on. We will assume that all the cash flows occur on the first day of the year.

Future Value = Year 1 Cash Flow*(1+Interest Rate)^5 + Year 2 Cash Flow*(1+Interest Rate)^4 + Year 3 Cash Flow*(1+Interest Rate)^3 + Year 4 Cash Flow*(1+Interest Rate)^2 + Year 5 Cash Flow*(1+Interest Rate)^1

Future Value after 5 Years = 85*(1+5.5%)^5 + 160*(1+5.5%)^4 + 230*(1+5.5%)^3 + 285*(1+5.5%)^2 + 255*(1+5.5%)^1 = $1,165.62

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Part b)

Present value is calculated by discounting the value of all of the future cash flows to today's value using the interest rate/discount rate.

Present Value = Year 1 Cash Flow/(1+Hurdle Rate)^1 + Year 2 Cash Flow/(1+Hurdle Rate)^2 + Year 3 Cash Flow/(1+Hurdle Rate)^3 + Year 4 Cash Flow/(1+Hurdle Rate)^4 + Year 5 Cash Flow/(1+Hurdle Rate)^5

Present Value = 85/(1+5.5%)^1 + 160/(1+5.5%)^2+ 230/(1+5.5%)^3 + 285/(1+5.5%)^4 + 285/(1+5.5%)^5 = $868.31

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Part c)

You need to calculate the NPV (Net Present Value) to determine as to whether the investment should be made or not. If NPV is positive, the project will be accepted otherwise not.

NPV = -Present Value of Costs + Present Value of Benefits (as calculated in part b)

NPV = -$950 + $868.31 = -$81.69 (no the investment should not be made, since NPV is negative)

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Part d)

IRR indicates the rate of return at which the NPV of an investment will be 0. In this case. It has been assumed that the Year 2 cash flow will be paid at the end of Year 2 only and not at beginning of Year 2. only Year 1 cash flow will be assumed to be paid today.

NPV = 0 = -Cash Outflow + Cash Inflow/(1+IRR)^1 + Cash Inflow/(1+IRR)^2 + Cash Inflow/(1+IRR)^3 + Cash Inflow/(1+IRR)^4+ Cash Inflow/(1+IRR)^5 the equation will change depending upon the expected cash inflows/outflows in any year)

IRR can be calculated with the use of EXCEL, details mentioned below:

IRR calculation

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Part e)

Payback period is the period within the investment made by the company get recovered with the cash inflows generated by the project.

In this case, the amount of $600 is the inital cost, which gets recovered as

Year 1 = $85, Year 2 = $160, Year 3 = $230 and the balance of $125 ($600 - $85 - $160 - $230) between Year 3 and Year 4.

Payback Period = Partial Recovery Year + Balance Amount/Cash Flow of the Year in which Investment is fully Recovered = 3 + 125/285 = 3.44 Years

Year 0 Cash Flow -85 Year 1 Cash Flow 0 Year 2 Cash Flow -160 Year 3 Cash Flow 230 Year 4 Cash Flow 285 Year 5 Cash Flow 255 IRR =IRR(-85,0,-160,230,285,255) = 50.64%

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