Time Value of Money

**Time Value of Money** Money today is worth more than the same amount in the future because money today can be invested to earn interest. Assume 10% Interest Rate (r). | Today | Year 1 | Year 2 | |---|---|---| | $1,000 | $1,100 | $1,210 | | PV | FV1 | FV2 | **Future Value** FV Factor = (1+r)^n * FV1 = PV x (1+r)^1 * FV2 = PV x (1+r)^2 * FVn = PV x (1+r)^n **Present Value** PV Factor = 1/(1+r)^n * PV = FV1 x 1/(1+r)^1 * PV = FV2 x 1/(1+r)^2 * PV = FVn x 1/(1+r)^n **Example 1:** How much will a $100,000 time deposit be worth after 12 years if it earns 10% interest per year? FV12 = 100,000 * 3.138 = $313,800 **Example 2:** How much do you need to invest in a time-deposit earning 10% interest per year to get $100,000 after 12 years? PV = 100,000 * 0.319 = $31,900 **3. How many years will it take for P100,000 to grow to be ₱293,700 if it is invested in an account that earns 8% interest per year?** 293,700 / 100,000 = 2.937 **14 years** **4. At what interest rate should ₱100,000 be invested so that it will grow to be ₱935,800 after 10 years?** 935,800 / 100,000 = 9.358 **15%** **Short Quiz (Blue: Missing Answer)** | Present Value | Future Value | Period (n) | Rate (r) | FV/PV Factor | |---|---|---|---|---| | 1. 250,000 | 370,000 | 10 years | 4% | 1.480 | | 2. 45,000 | 80,820 | 12 years | 5% | 1.796 | | 3. 307,480 | 500,000 | 10 years | 5% | 1.621 | | 4. 25,000 | 140,000 | 13 years | 14% | 3.181 | | 5. 1,000,000 | 1,311,000 | 4 years | 7% | 1.311 | | 6. 40,000 | 789,920 | 19 years | 17% | 19.748 | | 7. 50,000 | 56,200 | 2 years | 6% | 1.124 | | 8. 500,000 | 1,671,000 | 14 years | 9% | 3.342 | **CAPITAL BUDGETING & COST ANALYSIS** **Capital Budgeting:** Planning process used to determine whether a long-term investment is worth the funding. Has 5 Methods. **Primary OBJECTIVE:** Increase value of the company to shareholders. **Involves:** An initial cash outlay followed by a series of cash inflows. **Annual returns can be either even or uneven cash inflows (but mostly even)** **Example:** A university is considering to put up a cozy Starbucks coffee shop. The plan requires a cash outlay of P75 million & projected to generate annual net cash inflows of P36 Million. This project would involve a 3-year franchising agreement after which, SB would assume ownership. Should the university proceed with this investment? **Annual Net Income = 15,000,000** **Cash Flow Return on Investment (CFROI)** * Measures the average annual cash return over the life of the investment. * Involves a relatively simple calculation. * Ignores depreciation & time value of money. Formula: Average Annual Cash Inflow / Net Investment = 36,000,000 / 75,000,000 = 48% **2. Accrual Accounting Rate of Return (AARR)** * Measures Net Income generated from the investment. * Follows conventional Accounting concepts. * Considers Depreciation but Ignores time value of money. Formula: Average Annual Net Income / Net Investment = 15,000,000 / 75,000,000 = 15% or 14.66% **3. Payback Period** * Refers to the period of time required to recover the investment or to reach the break-even point. * Important for firms concerned with Liquidity. * Investments with shorter payback periods are better. * Ignores Depreciation & time value of money. **Two Types:** * Simple Payback: Reciprocal of CFROI (for EVEN) * Discounted Payback **Formula:** Net Investment / Annual Cash Inflows **Simple Uneven:** Years before full recovery + Remaining Unrecovered Investment / Cash flows during the year **In Millions:** | Y1 | Y2 | Y3 | Total | |---|---|---|---| | Annual Cash Inflows | 36 | 36 | 36 | 108 | | Unrecovered Inv. | 39 | 15 | 0 | Simple Uneven Payback = 2 + 15,000,000 / 48,000,000 = 2.3 years **Discounted Payback:** Use 11% discount rate | In Millions | Y0 | Y1 | Y2 | Y3 | Total | |---|---|---|---|---|---| | Net Investment | (15) | | | | (15) | | Annual Cash Inflows | | 36 | 36 | 36 | 108 | | Net Cash flows | (15) | 36 | 36 | 36 | (33) | | PV Factor (check 11%) | 1.000 | 0.901 | 0.812 | 0.731 | | PV Net Cash flows | (15) | 32.4 | 29.2 | 26.3 | (33) | | Unrecovered Inv. | 42.6 | 13.3 | | | Discounted Payback = 2 years + 13.3M / 26.3M = 2.5 years