Topic 2: The Time Value of Money Concept

The topic explores the concept of time value for money and why it may be important when business owners or firm management make financial decisions.

1. Time Value of Money Corporate Finance

2. Concept of Time Value of Money (TVM) Definition: The idea that money available today is worth more than the same amount in the future due to its potential earning capacity. This core principle underpins all areas of finance. Importance: TVM is foundational in valuing future cash flows, investments, and financing decisions. It reflects opportunity cost, inflation, risk, and return factors.

3. Present Value (PV) and Future Value (FV) Present Value (PV): The current value of a future sum of money or cash flows, discounted at a specific interest rate. Where; PV = Present value FV = Future value or expected cash flow r = Interest rate (per period) n = Number of periods  

4. Behavioural Finance and Time Value of Money Understanding the psychological factors that influence our financial decisions is crucial at personal & corporate levels. Hyperbolic discounting explains our tendency to prefer immediate rewards over larger future ones, even if the future rewards are objectively better. This bias can lead to suboptimal financial decisions, such as overspending and under-saving. Loss aversion is another psychological factor that can distort our judgment. We tend to overweight losses compared to gains, which can influence investment decisions, leading us to hold onto losing investments for too long.

5. Inflation and Time Value of Money Inflation erodes the purchasing power of money over time. Therefore, it's essential to distinguish between real interest rates and nominal interest rates. The real interest rate is the interest rate adjusted for inflation, while the nominal interest rate is the stated interest rate. To assess the true return on an investment, it's crucial to consider the real interest rate. Additionally, inflation-adjusted returns provide a more accurate measure of investment performance by accounting for the effects of inflation.

6. Risk and Time Value of Money Risk premiums are the additional returns investors require to compensate for the risk of an investment. These premiums are influenced by factors such as the riskiness of the investment, the investor's risk tolerance, and market conditions. Higher risk premiums lead to higher discount rates, which can affect the present value of future cash flows. Certainty equivalents are the amount of money an individual would be willing to accept today in exchange for a risky future cash flow. By understanding certainty equivalents, we can assess the riskiness of investments and make more informed financial decisions.

7. Practical Applications Time value of money concepts are essential for both personal and corporate finance. By understanding how the time value of money works, we can make better financial decisions and achieve our long-term goals. In personal finance , these concepts can be applied to; Retirement planning, Loan repayment, and Investment decisions.

8. In corporate finance , the time value of money is crucial such as in; Financial planning: Understanding the division of payments between interest and principal over the life of a loan (Loan amortization). Project Valuation: Using DCF (Discounted Cash Flow) to assess project viability. Investment Decisions: Evaluating various investment options by discounting future cash flows, has a direct effect on the firm capital budgeting process.

9. Future Value (FV): The value of a current asset at a future date, based on an assumed rate of growth. Where; FV = Future value; PV = Present value r = Periodic interest rate; n = No. of periods  

10. Ordinary Annuity A series of equal payments made at the end of each period. PV & FV of an Ordinary Annuity: P = Payment per period  

11. Annuity Due A series of equal payments made at the beginning of each period. PV & FV of an Annuity Due:  

12. Perpetuity Ordinary perpetuity (An annuity that lasts forever, with payments continuing indefinitely) PV of a Perpetuity; Perpetuity Due (payments made at the beginning of each period)  

13. Internal Rate of Return (IRR) IRR is the discount rate that makes the NPV of all cash flows from a particular project equal to zero That is, the rate at which the present value of cash inflows equals the present value of cash outflows. Since this equation can’t be solved algebraically for [r], IRR is typically found using iterative numerical methods. IRR Provides the percentage return expected from the investment.

14. IRR Formula where: = Cash flow at time, t r = IRR t = Time period n = Total number of periods  

15. Corporate Expansion Decision Imagine you are a financial manager at Tujijenge , a manufacturing company considering a new investment to expand production capacity. The project requires an initial outlay of Ksh50 million and is expected to generate the following cash flows over the next 5 years: Year 1: Ksh10 million Year 2: Ksh12 million Year 3: Ksh15 million Year 4: Ksh18 million Year 5: Ksh20 million

16. The company’s cost of capital is 10% per annum. Additionally, the expansion will be partially financed by a loan of Ksh30 million with an interest rate of 8%, repayable in equal annual instalments over 5 years. Required: Calculate the Net Present Value (NPV) of the Project: Discount each year’s cash flow back to its present value and subtract the initial investment. Determine if the project is financially viable based on the NPV rule.

17. 2. Determine the Internal Rate of Return (IRR): Identify the discount rate at which the NPV of the project equals zero. Compare this with the company’s cost of capital. 3. Create an Amortization Schedule for the Loan: Calculate the annual instalment amount using the annuity formula. Break down each instalment into interest and principal components.

18. 4. Analyze Different Scenarios: What if the cost of capital increases to 12%? How does it affect the NPV and IRR? Consider the impact if the annual cash flows fluctuate by ±10%. 5. Discuss the Decision-Making Process: Should the company proceed with the expansion? What qualitative factors might also influence this decision (e.g., market trends, competitive landscape)?

19. Net Present Value (NPV) of the Project: where: = Cash flow in year, t r = Cost of capital (10% or 0.10) n = Number of periods (5 years) Initial Investment = Ksh50 million  

20. 1. Discount Cash Flows:  

21. Calculate NPV: NPV = Total PV – Initial Investment PV = 9,090,909.09 + 9,917,355.37 + 11,270,982.73 + 12,294,350.14 + 12,416,118.29 − 50,000,000 NPV = Ksh54,989,715.62 − Ksh50,000,000 = Ksh4,989,715.62 Interpretation: Since the NPV is positive, the project is financially viable at a discount rate of 10%.

22. 2. Determine the Internal Rate of Return (IRR): The IRR is the discount rate that makes the NPV of the project zero. This is an Iterative Process : assume initial IRR = 15%  

23. Project NPV using IRR PV = 8,695,652.17 + 9,073,359.07 + 9,857,819.91 + 10,291,276.08 + 9,944,007.64 = 47,862,114.87 NPV = Ksh47,862,114.87 − Ksh50,000,000 = (Ksh2,137,885.13) Since NPV < 0 at 15%, IRR is between 10% and 15%. Iterating the process finds that IRR = 12.5%.

24. 3. Amortization Schedule for the Loan: Annual Payment: where: P = Annual Payment; r = 0.08 (8% interest rate) PV = 30M; n=5  

25. Amortization Schedule: Year Beginning Bal Interest (8%) Payment Principal Rep Ending Bal 1 30,000,000 2,400,000 7,514,003.86 5,114,003.86 24,885,996.14 2 24,885,996.14 1,990,879.69 7,514,003.86 5,523,124.17 19,362,871.97 3 19,362,871.97 1,549,029.76 7,514,003.86 5,964,974.10 13,397,897.87 4 13,397,897.87 1,071,831.83 7,514,003.86 6,442,172.03 6,955,725.84 5 6,955,725.84 556,458.07 7,514,003.86 6,957,545.79

26. Comparing Loan Interest Rate with Cost of Capital Given: Loan interest rate = 8% per annum Company's cost of capital = 10% per annum Comparison: The loan interest rate (8%) is lower than the company's cost of capital (10%). Conclusion: From a financial perspective, the loan interest rate is favorable for the firm; suggesting that it borrows money at a lower cost than the return it expects to earn on its investments. This has a positive effect in the overall financial health of the company.

27. 4. Analyze Different Scenarios: Scenario 1: Increase Cost of Capital to 12% Recalculate NPV using r = 12%. Impact: Lower NPV (approx. Ksh2,146,918.15 ), IRR stays constant, making the project less attractive but still viable. Scenario 2: Fluctuate Annual Cash Flows by ±10% Recalculate cash flows using the new values. Higher cash flows improve NPV, while lower cash flows decrease it.

28. 5. Decision-Making Process: Quantitative Analysis: At a 10% cost of capital, the project is viable ( NPV = Ksh 4,989,715.62 ). Qualitative Factors: Consider market trends, strategic fit, competitive landscape, and risk tolerance. Conclusion: The project is likely beneficial under current conditions, but management should monitor key risk factors, particularly changes in the cost of capital and cash flow forecasts.