Case Studies on Time Value of Money

 Case Study:1

Case Study: Making Investment Decisions using Time Value of Money

Company XYZ is a tech startup that has recently received a substantial funding round and is considering two investment opportunities. The company's financial analysts are tasked with evaluating these investment options using the concept of Time Value of Money (TVM) to determine the most profitable and beneficial choice.

Investment Option A: New Product Development The first investment option involves developing a new software product that is expected to revolutionize the market. The project requires an initial investment of $100,000, and it is estimated to generate a net cash flow of $30,000 per year for the next five years. After five years, the product is expected to become obsolete, and the cash flow will cease.

Investment Option B: Expanding Existing Business The second investment option is to expand the company's existing line of products and services. This expansion requires an initial investment of $150,000. The expansion is expected to generate a net cash flow of $40,000 per year for the next seven years.

The company's cost of capital, which represents the required rate of return for investments, is 10%.

Questions:

1.         Which investment option should Company XYZ choose based on the Net Present Value (NPV) criterion?

Solution: To evaluate the investment options using the Net Present Value (NPV) criterion, we need to calculate the present value of each option's cash flows and compare them to the initial investment.

a) Investment Option A: The cash flow for Investment Option A is $30,000 per year for five years, and the initial investment is $100,000. The discount rate is 10%.

Using the formula for the NPV calculation: NPV = Σ [CFt / (1 + r)^t] - Initial Investment

where: CFt = Cash flow in year t r = Discount rate t = T

ime period (in years)

NPV for Investment Option A: NPV = [($30,000 / (1 + 0.10)^1) + ($30,000 / (1 + 0.10)^2) + ($30,000 / (1 + 0.10)^3) + ($30,000 / (1 + 0.10)^4) + ($30,000 / (1 + 0.10)^5)] - $100,000

NPV = [$27,272.73 + $24,793.39 + $22,539.45 + $20,490.41 + $18,626.74] - $100,000 NPV = $113,722.72 - $100,000 NPV = $13,722.72

b) Investment Option B: The cash flow for Investment Option B is $40,000 per year for seven years, and the initial investment is $150,000. The discount rate is 10%.

NPV for Investment Option B: NPV = [($40,000 / (1 + 0.10)^1) + ($40,000 / (1 + 0.10)^2) + ($40,000 / (1 + 0.10)^3) + ($40,000 / (1 + 0.10)^4) + ($40,000 / (1 + 0.10)^5) + ($40,000 / (1 + 0.10)^6) + ($40,000 / (1 + 0.10)^7)] - $150,000

NPV = [$36,363.64 + $33,057.85 + $30,051.68 + $27,320.62 + $24,842.38 + $22,596.71 + $20,565.19] - $150,000 NPV = $194,797.67 - $150,000 NPV = $44,797.67

Conclusion: Based on the Net Present Value (NPV) criterion, Investment Option B (Expanding Existing Business) yields a higher NPV of $44,797.67, which indicates that it is a more profitable investment compared to Investment Option A (New Product Development) with an NPV of $13,722.72. Therefore, Company XYZ should choose Investment Option B to expand its existing business as it provides a higher return on investment.

Case Study:2

Case: Comparing Mortgage Alternatives

The application of the time value of money principles can help you make decisions on loan alternatives. This exercise requires you to compare three mortgage alternatives Notes using various combinations and points. Points on a mortgage refer to a payment that is made upfront to secure the loan. A single point is a payment of one per cent of the amount of the total mortgage loan. If you were borrowing 200,000 a single point would require an upfront payment of 2,000. When you are evaluating alternative mortgages, you may be able to obtain a lower rate by making an upfront payment. This comparison will not include an after-tax comparison. When taxes are considered, the effective costs are affected by interest paid and the amortization of points on the loan. This analysis will require you to compare only beforetax costs.

Zeal.com allows you to compare the effective costs on alternative mortgages. You are considering three alternatives for a 250,000 mortgage. Assume that the mortgage will start in December, 2006. The mortgage company is offering you a 6% rate on a 30-year mortgage with no points. If you pay 1.25 points, they are willing to offer you the mortgage at 5.875%. If you pay 2 points, they are willing to offer you the mortgage at 5.75%.

Questions

1. What are the mortgage payments under the three alternatives?

2. Which alternative has the lowest effective cost?

3. Can you explain how the effective rate is being calculated?