# Concepts of Present Value and Application

Part II: Concepts of present value and application to certainty cash flow

Note: It is recommended that you use a spreadsheet such as Excel in order to solve the following problems.

1. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $5,700.00 in one year. Account B will be worth $8,900.00 in two years. Both accounts earn 3.6% interest. What is the present value of each of these accounts? What is the present value of the two accounts together?

2. Suppose you just inherited an platinum mine. This platinum mine is believed to have three years worth of platinum deposit. The net income this oil filed is projected to bring you each year for the next three years:

Year 1: $46,000,000

Year 2: $74,000,000

Year 3: $67,000,000

Compute the present value of this stream of income at a discount rate of 5%. You are to arrive at the present value for a whole stream of income, i.e. the total value of receiving all three payments. This is actually the value of the platinum mine.

You compute this by computing the present value of each component of the cash flow (each year's proceeds) with regard to the time you receive the amount, and then add together the three present values in order to get the present value of the platinum mine. (See the example in the spreadsheet).

Now re-compute the present value of the income stream from the platinum mine, or the value of the platinum mine at a discount rate (or cost of capital of the company) of 12%. Re-compute it again using a discount rate of 10%, then at 8%, 6%, 4% and 2%. Compare the present values of the income stream under the different discount rates.

Show your calculations and write a short paragraph with conclusions from the computations.

3. The Net Present Value (NPV) criterion for investment decisions states that the organization should accept all investment projects whose NPV is positive. An alternative criterion is the Internal Rate of Return (IRR) criterion. The Internal Rate of Return (IRR) of a project is the discount rate at which the NPV of the project is exactly equal to zero. The internal rate of return can easily be computed using Excel spreadsheet: Insert the initial investment as a negative number in cell A1, and the net proceeds from the investment in cells B1, C1, D1 etc. Suppose there are 5 annual proceeds from the investment. Then you insert the five proceeds in cells B1, C1, D1, E1 and F1. In order to find the IRR of the investment you use a function that exists in Excel: Bring the cursor to cell G1, and type:

=irr(a1..f1,0.1) where a1..f1 is the range where you inserted the numbers, and 0.1 is a 'guess' that you must insert. (If you insert 0.0 that is also fine but you must insert a 'guess'.)

For example, if the initial investment is $1000, the annual proceeds are $200, $250, $300, $350 and $400 in 1, 2, 3, 4 and 5 years, then the spreadsheet will be as follows:

-1000 200 250 300 350 400 13.453% $101.24743

The number 13.435% is the IRR of the investment. The NPV at a discount rate of 0.10 (or 10%) is $101.24743.

The NPV is computed using the following function (in cell H1): 1.10*npv(0.10,A1..F1)

(a) Insert the numbers of the example in an Excel spreadsheet, insert the 'functions' and verify that you indeed obtain the same IRR of 13.453% and NPV at 10% of 101.24743.

(b) Suppose your company is considering the following investment proposal:

Invest now: -$17 million; 1 year from now the net cash inflow is $3.4 million; 2 years from now the net cash inflow is $3.4 million; 3 years from now the net cash inflow is $3.7 million; 4 years from now the company gets a net cash inflow of $9.7 million.

Compute and report the Internal Rate of Return (IRR) of the project (accurate to 2 digits after the decimal point) and the NPV at a discount rate of 8% (0.08). The discount rate of 8% in this case is also called "The Cost of Capital of the organization".

Suppose your company's cost of capital is indeed 8%. Would you recommend that the organization should undertake the project based on the IRR criterion? Based on the NPV criterion? Explain.

(c) Compute and report also on the NPV of the same investment for alternative costs of capital (discount rates) of 0% (0.00), 4% (0.04), 8% (0.08), 12% (0.12) and 16% (0.16). You may plot a diagram where on the horizontal axis you mark the discount rate or the cost of capital, and on the vertical axis the Net Present value of the proposed investment. What trend do you observe in the NPV as a function of the cost of capital of the firm?

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Part II: Concepts of present value and application to certainty cash flow

Note: It is recommended that you use a spreadsheet such as Excel in order to solve the following problems.

1. Suppose you have two bank accounts, one called Account A and another Account B. Account A will be worth $5,700.00 in one year. Account B will be worth $8,900.00 in two years. Both accounts earn 3.6% interest. What is the present value of each of these accounts? What is the present value of the two accounts together?

Account A

PV = FV/(1 + i)n where PV is the present value

FV is the future value

i is the interest rate

n is the period

PV = 5,700/(1 + 0.036)1

= 5,501.93

Account B

PV = 8,900/(1 + 0.036)2

= 8,292.21

Present value of the two accounts = 13,794.14

2. Suppose you just inherited an platinum mine. This platinum mine is believed to have three years worth of platinum deposit. The net income this oil filed is projected to bring you each year for the next three years:

Year 1: $46,000,000

Year 2: $74,000,000

Year 3: $67,000,000

Compute the present value of this stream of income at a discount rate of 5%. You are to arrive at the present value for a whole stream of income, i.e. the total value of receiving all three payments. This is actually the value of the platinum mine.

You compute this by computing the present value of each component of the cash flow (each year's proceeds) with regard to the time you receive the amount, and then add together the three present values in order to get the present value of the platinum mine. (See the example in the ...

#### Solution Summary

This solution is comprised of a detailed explanation to answer the present value of each account and present value of both accounts and compute IRR and NPV for the cash flows.