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Chapter 3: The Economic Evaluation of Investment

Proposals

1. Time Value of money

2. Net present value (NPV)

3. Graphical representation of NPV

4. Internal rate of return (IRR)

5. An economic rationale for IRR rule

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Time Value of Money Definition: A rationale human being would not

value the opportunity to receive a specific amount of money today equally with the opportunity to have the same amount at some future date. Most human beings value the opportunity to receive money now higher than receive one or two years from now the same amount. The additional amount that is required for receiving after a certain time period in future than the amount received today is known as time value of money. That is this additional amount is given as value of time waiting. Actually the percentage change in value of a certain amount of money for a certain time period gap is known as time value of money

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Rationale for Time Value of Money

Time value of money is existed for the following reasons: Future uncertainty Sacrifice present consumption or preference

for higher consumption in future period Alternative investment opportunities i.e.

opportunity cost. Sacrifice of cash holding preference Inflation

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Terminologies

Present value: The value of today that is obtained by discounting a future cash flow or a series of cash flows by the opportunity cost of fund as discount rate.

Future value: The amount or value will be obtained at a certain time point in future of a cash flow or a series of cash flows by compounding at a given interest rate or opportunity cost over a certain time period.

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Terminologies

Discounting: The process of finding the present value of a cash flow or a series of cash flows by using a given discount rate.

Compounding: The arithmetic process of determining the final value of a cash flow or a series of cash flows by using a certain interest rate

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Terminologies

Simple interest rate: The interest rate that charged only on the principal amount for a specific period is called simple interest rate.

Compound interest rate: The interest rate that is charged both on principal and interest amount period to period is called compound interest rate.

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Terminologies

Installment: Periodic payments or receipts related to any transaction or contract are known as installment.

Annuity: The equal amount of cash flow incurred at equal time interval is called annuity.

Annuity due: The annuity under which the cash flow is incurred at the beginning of each period is called annuity due.

Annuity immediate: The annuity under which the cash flow is incurred at the end of each period is called annuity immediate.

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Terminologies

Perpetuity: The annuity under which the cash flow is incurred for a infinite period of time is called Perpetuity..

Nominal interest rate: Rate of interest stated in an agreement for transferring fund from one party to another party is known as nominal interest rate.

Effective interest rate: Rate of interest ultimately paid by the user of fund to the supplier of fund by taking into consideration of timing frequencies and other charges is known as effective interest rate.

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Definition of capital investment techniques

1. NPV: NPV is defined as the summation of the present values of cash flows after tax in each year over the project or investment period minus the summation of present values of net cash outflows in each year during that period.

2. NPV Profile: The graphical presentation of relationship between a project’s and the firm’s cost of capital or discount rate is called NPV profile. A graph that plots a project’s NPV against the discount rates is defined as the project’s NPV profile.

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Definition3. IRR: The discount rate that makes equal the present

value of a project’s future cash inflows to the present value of its total costs. Equivalently the rate that forces the net present value to equal zero is internal rate of return.

4. Modified IRR: The discount rate at which the present value of a project’s cost is equal to the present value of its terminal value, where the terminal value is found as the sum of the future values of cash inflows, compound at the firm’s cost of capital.

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Definition5. Net Terminal Value: When terminal amount of any

project obtained from reinvestment is discounted into present value at a certain required rate of return and the present value of cash outlays is deducted from the first, then the net result is known as net terminal value.

6. Profitability Index: It measures the present value of returns per unit of investment is called profitability index. It is defined as the ratio that is obtained dividing the present value of future cash inflows by the present values of cash outflows.

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ExampleAn asset can be purchased for Tk.7,50,000 that will

provide net benefits Tk.1,00,000; Tk.3,00,000; Tk.2,10000 & Tk.280000 in years 1, 2, 3 & 4 respectively. Reinvestment rate is 8% and cost of capital is 10.5%.Would it be wise to purchase the asset under the following techniques?(i) NPV (ii) IRR (iii) PI (iv) MIRR(v) NTV

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An Economic Rationale for NPV Rule

1. It recognizes time value of money.2. It considers all cash flows occurring over

the entire life of the project to calculate its rate of return.

3. It is consistent with the shareholders’ wealth maximization goal.

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An Economic Rationale for NPV Rule

4. It does not use the concept of required rate of return.

5. It is easily understandable to the business executives and non-technical people.

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An Economic Rationale for IRR Rule

If the internal rate of return exceeds the cost of capital of the fund used to finance a project, a surplus remains after paying for the capital and this surplus accrues to the firm’s stockholders. Therefore, taking on a project whose IRR exceeds its cost of capital increases the value of the firms’ stock.

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Traditional measures of investment worth

Payback Period Method: Payback method means how many years will it take for the cash benefits to pay the original cost of an investment, normally disregarding salvage value. It measures the number of years required for the cash flow after tax to payback the original outlay required in an investment proposal. If the project generates constant annual cash flows, the payback period can be computed by dividing cash outlay by annual cash inflow.

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Traditional measures of investment worth

Discounted Payback Period: The length of time required for an investment’s discounted cash flows to equal its initial cost is known as discounted payback period. Based on discounted payback rule, an investment is acceptable if its discounted payback is less than some pre-specified number of years.

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Traditional measures of investment worthExample of payback and discounted payback:

Year

Cash flows Cum cash flows Initial cost is Tk.300000; cost of capital is 12.5%

Payback =3 yearsDiscounted payback=4 years (apprx)

Undisc Disc Undisc Disc

1 100000

88889

100000

88889

2 100000

79012

200000

167901

3 100000

70233

300000

238134

4 100000

62430

400000

300564

5 100000

55493

500000

356057

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Traditional measures of investment worth

Average/Accounting Rate of Return: The accounting rate of return also known as the return on investment, uses accounting information as revealed by financial statement to measure the profitability of an investment. It is found by dividing the average after tax profit by the average investment. The average investment would be equal to half of the original investment if it is depreciated constantly.

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Traditional measures of investment worth

Example of Average/Accounting Rate of Return: Required investment is Tk.500000 and project life expectancy is 5 years. Expected net income after-tax are Tk.100000, Tk.150000, Tk.50000, Tk.0 & (Tk.50000) in next 5 years. Average net income is Tk.50000 and average investment/book value is Tk.250000. So average rate of return is 20%.

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Problems

1. What will be present value of Tk.500000 will be received 8 years from now at 15% discount rate?2. Find the present value of Tk.20000, Tk.25000, Tk15000 and Tk.30000 will be received in years 0, 1, 2 & 3 respectively by considering discount/compound rate is 10%. 3. Find the present value of Tk.50000, Tk.28000, Tk.52000 and Tk.40000 will be received in years 1, 2, 3 & 4 respectively by considering discount/compound rate is 10%. 4. You have a choice of receiving 10 payments of Tk.85000 a year, with the first payment to be received one year from now, or Tk.500000 in cash today. If your opportunity cost is 12%, which would you prefer?

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Problems

5. You have a choice of receiving 15 payments of Tk.50000 a year, with the first payment to be received just now, or Tk.600000 at a time today. If your opportunity cost is 15% which would you prefer? 6. RIC Inc. manufactures and sells tobacco products in the market. The company receives about Tk.200000 cash flow each year from the product after all expenses, including taxes. Samson Ltd has recently offered to buy the product for Tk.1500000. RIC’s opportunity cost is 11%. Should it sell the product if it thinks its life expectancy is indefinitely long? 7. What will be future value of Tk.300000 deposited in a bank after 5 years from now at 9% interest rate?

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Problems

8. Find the future value of Tk.10000, Tk.30000, Tk.45000 and Tk.60000 will be received in years 0, 1, 2 & 3 respectively by considering compound rate of 11%. 9. Find the future value of Tk.30000, Tk.20000, Tk.25000 and Tk.30000 will be received in years 1, 2, 3 & 4 respectively by considering compound rate of 10.5%. 10. ou have a choice of receiving 5 payments of Tk.150000 a year, with the first payment to be received one year from now or Tk.500000 at a time at the end of the total period. If your opportunity cost is 12% which would you prefer?

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Problems

11. You have a choice of receiving 10 payments of Tk.50000 a year, with the first payment to be received just now, or Tk.750000 at a time at the end of the total period. If your opportunity cost is 13%, which would you prefer?  12. Contractual interest rate in a loan agreement is 16% and loan processing fee is 2%. What is the effective interest rate of the loan if interest is compounded monthly?

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HomeworkQuestions & problems:3.5, 3.6, 3.12 & 3.14