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Real versus Nominal Dollars. Your consulting firm will produce cash flows of \(\$ 100,000\) this year, and you expect cash flow to keep pace with any increase in the general level of prices. The interest rate currently is 8 percent, and you anticipate inflation of about 2 percent. a. What is the present value of your firm's cash flows for Years 1 through 5? b. How would your answer to (a) change if you anticipated no growth in cash flow?

Short Answer

Expert verified
a. The present value of the firm's cash flows for Years 1 through 5, with inflation, is the sum of present values calculated in Step 4. \n b. The present value of the firm's cash flows for Years 1 through 5, with no growth, is the sum of present value calculated in Step 5.

Step by step solution

01

Calculate Present Value with Inflation

Start by understanding that the cash flows increase each year with the inflation rate. The cash flow for year \(n\) can be obtained by multiplying the cash flow of the previous year with \(1+ inflation rate\). The present value \(PV_n\) for the cash flow at year \(n\) can be calculated as \(PV_n = Cash Flow_n / ( 1 + interest rate)^n\). Calculate \(PV_n\) for each of the five years and sum them up to get the total present value.
02

List Cash Flows for Each Year

Now, calculate the cash flow for each of the five years. Start with a cash flow of \$100,000 for year 1. For subsequent years, multiply the cash flow of the previous year with \(1+0.02\) i.e., \(1+ inflation rate\). Calculate the cash flow for each year and note them down.
03

Calculate Present Values for Each Year

Next, calculate the present value for cash flow of each year. Use the formula \(PV_n = Cash Flow_n / (1 + 0.08)^n\) i.e., \(PV_n = Cash Flow_n / (1 + interest rate)^n\). Calculate the present value for each year and note them down.
04

Add Up the Present Values

Now, sum up the present values for all five years to find the total present value of the firm's cash flows for Years 1 through 5. The obtained sum is the answer to part (a).
05

Calculate Present Value with No Growth

The procedure for calculating the present value with no growth is similar to that of Step 3, but now your cash flow is constant for each year. The cash flow for each year is $100,000. Calculate the present value for each year and sum them to find the total present value. This will answer part (b).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Inflation Rate
When we talk about inflation rate, we're referring to the percentage increase in prices over time. Inflation decreases the purchasing power of money, meaning that each dollar buys less over time. This is important when calculating the present value of future cash flows because it affects how much those flows are actually worth today.

In the exercise, the cash flow is expected to increase by 2% each year to match inflation. This means that if something costs $100 today, it will cost $102 next year. When you account for this expected change, you ensure that your cash flow estimates are in real terms, maintaining their purchasing power over time.

Understanding inflation is crucial as it helps businesses and individuals maintain the value of their money, ensuring they can buy the same amount of goods and services in the future.
Cash Flow
Cash flow refers to the money that your business is expected to generate over a certain period. It's vital for assessing the health and profitability of a business. In this exercise, your firm generates $100,000 in cash flow this year, and it's expected to grow with inflation.

Cash flows are expected to cover necessary expenses and generate profits, making it essential to accurately predict their future values. In practical terms, managing cash inflow and outflow is crucial for effective financial planning.

When calculating cash flows for future years, incorporate expected changes such as inflation. By doing this, the projections remain relevant and grounded in the expected economic environment.
Interest Rate
The interest rate represents the cost of borrowing or the benefit of saving money. It directly influences the calculation of present value, as it determines the discount rate applied to future cash flows.

In the exercise, an 8% interest rate is used to discount future cash flows. This reflects the opportunity cost of investing money now versus later. Higher interest rates decrease the present value of cash flows, meaning future money is worth less today.

Understanding interest rates is key to making informed investment decisions. It offers a way to compare different financial instruments and assess risks effectively by determining how much returns need to be weighed against potential losses due to future economic conditions.
Real vs Nominal Dollars
When we compare real vs nominal dollars, we're referring to the adjustment of money value for inflation. Nominal dollars refer to the face value of money without adjusting for inflation, while real dollars take into account the purchasing power over time.

In the context of this exercise, the firm anticipates cash flows that are "real dollars," meaning they grow with inflation. This distinction is crucial because it ensures calculations reflect true economic value, not just face value unaffected by inflation.

Understanding the difference helps make accurate financial assessments and ensures fair financial comparisons over time. It aids in determining actual growth and purchasing power, which are essential for strategic planning and valuation.

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Most popular questions from this chapter

Calculating Interest Rate. Find the interest rate implied by the following combinations of present and future values: $$\begin{array}{ccc} \text { Present Value } & \text { Years } & \text { Future Value } \\ \hline \$ 400 & 11 & \$ 684 \\ \$ 183 & 4 & \$ 249 \\ \$ 300 & 7 & \$ 300 \\ \hline \end{array}$$

Compound Interest. Old Time Savings Bank pays 5 percent interest on its savings accounts. If you deposit \(\$ 1,000\) in the bank and leave it there, how much interest will you carn in the first year? The second year? The tenth year?

Annuities and Interest Rates. Professor's Annuity Corp. offers a lifetime annuity to retiring professors. For a payment of \(\$ 80,000\) at age \(65,\) the firm will pay the retiring professor \(\$ 600\) a month until death. a. If the professor's remaining life expectancy is 20 years, what is the monthly rate on this annuity? What is the effective annual rate? b. If the monthly interest rate is .5 percent, what monthly annuity payment can the firm offer to the retiring professor?

Future Values. In 1880 five aboriginal trackers were each promised the equivalent of 100 Australian dollars for helping to capture the notorious outlaw Ned Kelley. In 1993 the granddaughters of two of the trackers claimed that this reward had not been paid. The Victorian prime minister stated that if this was true, the government would be happy to pay the S100. However, the granddaughters also claimed that they were chtitled to compound interest. How much was each entitled to if the interest rate was 5 percent? What if it was 10 percent?

Annuity Due. A store offers two payment plans. Under the installment plan, you pay 25 percent down and 25 percent of the purchase price in cach of the next 3 years. If you pay the entire bill immediately, you can take a 10 percent discount from the purchase price. Which is a better deal if you can borrow or lend funds at a 6 percent interest rate?

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