Business Investment Decisions
5.3 Discounted Cash Flow (DCF): Formula Approach
A. Introduction
Investment decisions are among the most critical choices facing business managers and investors because they determine the future profitability and sustainability of projects, assets, or entire firms. The right investments can lead to substantial growth and profits, while poor choices can lead to losses and strategic setbacks. Given the significant amounts of money and the long-term implications involved, these decisions require careful analysis and consideration.
When making investment decisions, it is crucial to consider the time value of money, as cash flows from an investment occur at different times in the future and cannot be directly compared due to their differing time periods. Money today has a different value than money tomorrow or years down the line, primarily due to interest. To address this, the concept of present value, discussed in previous chapters, becomes indispensable. By discounting future cash flows back to their present value using a suitable discount rate, we can accurately assess and compare the worth of these cash flows as if they occurred today. This process of discounting ensures that the value of money is standardized to the present moment, allowing for a fair and direct comparison between different investments.
To navigate business investment decisions, several financial appraisal methods have been developed. Each offers a unique perspective on the value and potential of an investment opportunity. This chapter introduces and explores two methods widely used in business and finance: Discounted Cash Flow (DCF) and Net Present Value (NPV).
Cash flows in business investments refer to the streams of cash that are expected to be received or paid out over the lifetime of the investment. They are the lifeblood of any financial analysis and the primary focus of valuation techniques such as NPV and DCF.
Cash Inflows are the amounts of money expected to be received from the investment. For a business, this could include revenue from sales of goods or services, returns on other investments, sale of assets, or any form of income or capital gains.
Cash Outflows represent the expenditure or costs associated with maintaining and operating the business or making an investment. This can include initial capital expenditures, ongoing operational costs, taxes, maintenance expenses, loan repayments, and any other forms of spending necessary to sustain the business or investment.
B. Discounted Cash Flow (DCF) Method
The DCF method estimates an investment’s value by discounting each of its expected future cash flows back to its present value at a focal date (usually ‘now’) using a discount rate, known as the required rate of return. This rate reflects the risk and the time value of money — essentially, the return that could be earned if the money was invested elsewhere with a similar risk profile. The sum of these present values provides the total value of the cash flows, which is considered the intrinsic value of the investment.
[asciimath]PV_(All \ Cash \ Flows)[/asciimath] [asciimath]=PV_(Cash \ flow \ 1)+[/asciimath] [asciimath]PV_(Cash \ flow \ 2)+...[/asciimath]Formula 5.1
If the DCF value is greater than the initial cost of the investment, the investment is considered acceptable. This means the investment is expected to generate a return above the discount rate, covering the cost of capital and providing additional value.
A delivery company is considering investing $30,000 in a project. The expected returns from this investment are projected to be $8,000 in one year, $13,000 in two years, and $16,000 in three years. The company’s required rate of return for investments is 8%. Calculate the discounted cash flow and determine whether this is a worthwhile investment.
Show/Hide Solution
- Required rate of return: [asciimath]I//Y=8%[/asciimath]
- The frequency of compounding periods is not provided, so it is assumed annually: [asciimath]P//Y=C//Y=1[/asciimath]
- Interest rate per compounding period: [asciimath]i = (I//Y)/(C//Y) = (8%)/1 =8%=0.08[/asciimath]
- Cost of capital [asciimath]=30,000[/asciimath]
- Cash flow 1: [asciimath]FV_1=8000[/asciimath]
- cash flow 2: [asciimath]FV_2=13,000[/asciimath]
- Cash flow 3: [asciimath]FV_3=16,000[/asciimath]
- Cash flow 1 time: [asciimath]t_1=1[/asciimath] year; [asciimath]N_1=C//Y*t_1=1[/asciimath]
- Cash flow 2 time: [asciimath]t_2=2[/asciimath] years; [asciimath]N_2=2[/asciimath]
- Cash flow 3 time: [asciimath]t_3=3[/asciimath] years; [asciimath]N_3=3[/asciimath]
It is important to note that all the cash flows in this scenario are returns on investment, meaning they are cash inflows. Given the need to make an immediate decision on the investment opportunity, we use ‘now’ as the focal date to determine the present values of the future cash flows. Starting with Formula 5.1, we will apply the present value formula from compound interest (Formula 2.4c) to calculate the present value of each expected cash inflow from the investment.
[asciimath]PV_(All \ Cash \ Flows)[/asciimath] [asciimath]=PV_(Cash \ flow \ 1)+[/asciimath] [asciimath]PV_(Cash \ flow \ 2)+[/asciimath] [asciimath]PV_(Cash \ flow \ 3)[/asciimath]
[asciimath]=FV_1(1+i)^(-N_1)+FV_2(1+i)^(-N_2) +FV_3(1+i)^(-N_3)[/asciimath]
[asciimath]=8000(1+0.08)^-1+13,000(1+0.08)^-2 +16,000(1+0.08)^-3[/asciimath]
[asciimath]=7407.407...+11,145.405...+12,701.314...[/asciimath]
[asciimath]~~$31,254.13[/asciimath]
Therefore, the discounted cash flow of the project is $31,254.13, which is greater than the cost of capital of $30,000. The returns are sufficient to cover the cost of capital and provide an additional value, indicating the company should proceed with the investment project under the given financial criteria.
Try an Example
The CEO of an ice cream company is choosing between two investment options: Project A and Project B. Both projects require the same initial investment. Project A is expected to yield returns of $45,000 in one year and another $45,000 in two years. In contrast, Project B is anticipated to bring in $10,000 in one year and $80,000 in two years. With the company’s required rate of return set at 12%, which project should the CEO choose based on the financial viability and the expected returns of each option?
Show/Hide Solution
- Required rate of return: [asciimath]I//Y=12%[/asciimath]
- The frequency of compounding periods is not provided, so it is assumed annually: [asciimath]C//Y=1[/asciimath]
- Interest rate per compounding period: [asciimath]i = (I//Y)/(C//Y) = (12%)/1 =12%=0.12[/asciimath]
Project A:
For Project A, both anticipated cash flows are returns on the investment, categorizing them as cash inflows. To determine the present values of these future cash inflows, we have two methods:
Using the Present Value Formula for Compound Interest: We can calculate the present value of each expected cash inflow individually by applying the formula for compound interest (Formula 2.4c). This involves discounting each future cash inflow back to its present value based on the specified discount rate.
Using the Present Value Formula for an Ordinary Simple Annuity: Alternatively, as both cash inflows from Project A are of equal amounts and are expected to occur at regular intervals (one year apart), they can be treated as payments of an ordinary simple annuity. In this case, we can apply the present value formula for an ordinary simple annuity (Formula 3.9a) to calculate the combined present value of both cash inflows in a single step. We use the second method here.
- Cash inflows 1,2: [asciimath]PMT=45,000[/asciimath]
- Annuity term: [asciimath]t=2[/asciimath] years
- One payment per year, so [asciimath]P//Y=1[/asciimath]
- Number of payments in the term: [asciimath]N=P//Y*t=1(2)=2[/asciimath]
[asciimath]PV_(All \ Cash \ Flows)[/asciimath] [asciimath]=[/asciimath] [asciimath]PV_("Annuity")[/asciimath]
[asciimath]=[/asciimath] [asciimath]PMT[(1-(1+i)^-N)/i][/asciimath]
[asciimath]=45,000[(1-(1+0.12)^-2)/0.12][/asciimath]
[asciimath]~~$76,052.30[/asciimath]
Therefore, the discounted cash flow of Project A is $76,052.30.
Project B:
Both cash flows in Project B are also returns on investment, meaning they are cash inflows. We apply the present value formula from compound interest (Formula 2.3c) to calculate the present value of each expected cash inflow from the investment.
- Cash flow 1: [asciimath]FV_1=10,000[/asciimath]
- cash flow 2: [asciimath]FV_2=80,000[/asciimath]
- Cash flow 1 time: [asciimath]t_1=1[/asciimath] year; [asciimath]N_1=C//Y*t_1=1[/asciimath]
- Cash flow 2 time: [asciimath]t_2=2[/asciimath] years; [asciimath]N_2=2[/asciimath]
Using Formula 5.1, we have
[asciimath]PV_(All \ Cash \ Flows)[/asciimath] [asciimath]=PV_(Cash \ flow \ 1)+[/asciimath] [asciimath]PV_(Cash \ flow \ 2)[/asciimath]
[asciimath]=FV_1(1+i)^(-N_1)+FV_2(1+i)^(-N_2)[/asciimath]
[asciimath]=10,000(1+0.12)^-1+80,000(1+0.12)^-2[/asciimath]
[asciimath]=8928.571...+63,775.510...[/asciimath]
[asciimath]~~$72,704.08[/asciimath]
Therefore, the discounted cash flow of Project B is $72,704.08.
Make a Decision:
The CEO should choose the project with the higher discounted cash flow value because it represents a greater return on investment after considering the time value of money at the company’s required rate of return. In this case, since Project A has a higher DCF value than Project B, the CEO should opt for Project A as the investment choice.
Try an Example
Section 5.3 Exercises
- A delivery company is considering investing $26,260 in a project. The expected returns from this investment are projected to be $6,000 in 1 year, $10,000 in 5 years, and $17,500 in 8 years. The company’s required rate of return for investments is 4.5%. a) Calculate the discounted cash flow. b) Is the investment worthwhile?
Show/Hide Answer
a) DCF = $26,071.88
b) No, it is not since DCF is less than the investment capital.
- The CFO of a company is choosing between two investment options: Project A and Project B. Both projects require the same initial investment. Project A is expected to yield returns of $35,000 in one year and another $35,000 in two years. In contrast, Project B is anticipated to bring in $29,000 in one year and $39,000 in two years. The company’s required rate of return is set at 8%. a) Calculate the discounted cash flow of Project A. b) Calculate the discounted cash flow of Project B. c) Which project should the CFO choose based on the discounted returns of each option?
Show/Hide Answer
a) Project A: DCF = $62,414.27
b) Project B: DCF = $60,288.07
c) Project A should be chosen because of the higher DCF.
- A company is considering two investment opportunities. Alternative 1 will result in payments of $9,000 in two years and $22,000 in four years. Alternative 2 will result in annual payments of $4,500 at the end of each year for a total of five years. The company’s required rate of return is 6.58%. a) Calculate the DCF of Alternative 1. b) Calculate the DCF of Alternative 2. c) Which investment alternative should the company choose to maximize its financial benefit? Round your answers to the nearest dollar.
Show/Hide Answer
a) Alternative 1: DCF = $24,973
b) Alternative 2: DCF = $18,660
c) Alternative 1 should be chosen because of the higher DCF.
