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Discounted Cash Flow

Additional Clarification

11 March 2014

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Background

A number of students have had very limited exposure to the concepts

behind discounted cash flow in their past A number of students do not use spreadsheets regularly

It became clear in the exam prep/Q&A session that some studentswere experiencing difficulty understanding the concepts

This short presentation will use one of the past exam questions to go

through the calculationsNOT the additional analysis required toanswer the remainder of the question.

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Basic Concepts

See Collier (4thedition ) Chapter 14.

Money now is worth more than money in the future. A future cash flowis worth less (in todays money) than if the cash flow occurred now.

Money in hand now could be invested at current interest rates. Eg $100 invested now at an annualinterest rate of 10% is equivalent to $110 (100+ 10% of 100) in 1 years time and $121 (110 +10%of 110)in 2 years time.

Similarly $100 in one years time is equivalent to $91 now using the same interest rate

Discounted cash Flow discounts future cash flow to their present value equivalent.

The discount factor can be derived from:

a pre calculated table (page 289 Collier 4thedition)

calculated directly

Using a pre set up spreadsheet

The formula for a discount factor is 1/ (1+r)n where r is the interest rate and n in the number of

periods in the future. Eg. The NPVdiscount factor for a cash flow in 2 years with an interest rate of 10% would be

1/(1+0.1)2 = 1/1.21 = 0.8264

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Calculations

Cash flows from info provided (in $,000)

Year Cash Flow Discount factor (15%) NPV

0 (investment) -440 -440.00

1 80 0.870 69.60

2 120 0.756 90.72

3 160 0.658 105.2

4 160 0.572 91.52

5 160 0.497 79.52

Total -3.44

Interest Rate 15.00%Project 1

Description Year Cash Flow DiscountFactor

Present

ValueInvestment Expenditure 0 -440 1.0000 -440.00income/expense 1 80 0.8696 69.57income/expense 2 120 0.7561 90.74income/expense 3 160 0.6575 105.20income/expense 4 160 0.5718 91.48income/expense 5 160 0.4972 79.55income/expense 1.0000 0.00income/expense 1.0000 0.00income/expense 1.0000 0.00income/expense 1.0000 0.00NET PRESENT VALUE -3.47

Using table on exam question3 decimal places

Using spreadsheet

4 decimal places

a) The calculation shows a Net Present Value forthe investment of $ -3,440 (-3,470)I.e. it fails to meet the hurdle rate of 15%.

b) If the price for the equipment could benegotiated down by at least $3,440 (3,470) theinvestment would show a zero/positive NPV at thehurdle rate of 15%. NPV at other interest ratescould be calculated to show sensitivity. IRR couldbe calculated to show actual rate of return(easiest with spreadsheet)