# Chapter 4 : Time Value of Money and Discount Factor

How many millionaires do you know who have become wealthy by investing in savings accounts ? I rest my case.

Robert G Allen

The Intrinsic Value of an investment is the discounted value of anticipated cash flows.

What is Time Value of Money ?

Time Value of Money explicitly incorporates the idea that a dollar received today is worth more than a dollar to be received a year from now because today's dollar can be invested to earn a rate of return over the next year. Essentially, the link between Income and Capital is the Rate of Return as the percentage of premiums paid at one date in terms of money to be on hand one year later.

What is Discount Factor ?

Discount Factor is the rate at which the future cash flows are multiplied to arrive at the present value of cash flows. The Rate of Return or Discount Rate not only includes compensation for bearing risk but also the expected rate of inflation. For example if the Rate of Return is 10% then the discount factor for year 1 is 0.909 (1/1.1) and for year 2 it is 0.826 (1/1/21).

Table 3 illustrates the Time Value of Money and compute the Intrinsic Value of cash flows for 100 Years based on the following assumptions:

Assumptions

 Cash Flows in Prior Period 100 CAGR of Cash Flows (1st to 10th Year) 15% Terminal Period Cash Flows will grow at an Inflation of 3% for 11th to 100th Year 3% Discount Rate or Cost of Capital 10%

I have taken a discount rate of 10%, so the next year if we reinvest 1, it should become 1.1 and then 1.21 and so forth. Thus, the Time Value of Money today for Year 1 is (1/1.1) or 0.909, (1/1.21) or 0.826 for Year 2, and so forth. Using this Discount Factor, we need to multiply the cash flows with the discount factor to arrive at the present value.

Intrinsic Value explicitly incorporates the idea that a dollar received today is more than a dollar to be received a year from now because today's dollar can be invested to earn a rate of return over the next year.

## Present Value of Cash Flows

The cash flows have been divided into two parts - Forecast Period and Terminal Period.

In the Forecast Period, the Cash Flow is 100 in Year Zero and is assumed to grow at 15% compounded for 10 Years. Then, during the Terminal Period, it is assumed to grow at an inflation rate of 3%.

The cash flows have then been multiplied by the discount factor (discount rate is taken at 10%) for that year to arrive at the present value for that year. Then, we sum all the present values to arrive at the Cumulative Present Value of Cash Flows (Years 1 – 100) which gives us the Capitalized Value of the Cash Flows at a Discount Rate of 10%.

Table 3
 Time Value - Cash Flows Forecast Period Terminal Period Year Cash Flows Growth Discount Rate - 10% Discount Factor PV of Cash Flows Year Cash Flows Inflation 3% Discount Rate - 10% Discount Factor PV of Cash Flows 0 100 1 115 15% 1.10 0.909 105 11 417 3% 2.85 0.350 146 2 132 15% 1.21 0.826 109 12 429 3% 3.14 0.319 137 3 152 15% 1.33 0.751 114 13 442 3% 3.45 0.290 128 4 175 15% 1.46 0.683 119 14 455 3% 3.80 0.263 120 5 201 15% 1.61 0.621 125 15 469 3% 4.18 0.239 112 6 231 15% 1.77 0.564 131 16 483 3% 4.59 0.218 105 7 266 15% 1.95 0.513 137 17 498 3% 5.05 0.198 98 8 306 15% 2.14 0.467 143 18 512 3% 5.56 0.180 92 9 352 15% 2.36 0.424 149 19 528 3% 6.12 0.164 86 10 405 15% 2.59 0.386 156 20 544 3% 6.73 0.149 81 - - 99 5617 3% 12528 0.00008 0.448 100 5785 3% 13781 0.00007 0.42 Cumulative Present Value of Cash Flows - Forecast Period 1287 Cumulative Present Value of Cash Flows - Terminal Period 2291 Present Value of Cash Flows - Forecast + Terminal 3578

The Present Value of Cash Flows during the forecast period is 1287 and during the terminal period (post the forecast period) is 2291. The sum of forecast and terminal period is 3578, which is the Intrinsic Value.