NPV, IRR and Investment Appraisal Time Value of Money · The present value (PV) of a future cash flow (FV) depends upon its: • Size . Timing - earlier cash flows are worth more today than later cash flows · Riskiness - lower risk cash flows are worth more today than higher risk cash flows Present Value of Single Cash Flows PV = FV (1+r){ Present Value= (1+ Discount Rate) Future Cash Flow ) Time E Years Or PV =- FV (1 +r)- · Using a scientific calculator: · Formula: PV = FV + (1+ r)' or FV(1 + r)* · Calculate the present value of £3,000 received in 3 years time if the discount rate is 9.5% (lower risk) · PV = 3000 = (1.0953) => 3000 = 1.313 = £2,285 · PV = 3000 x (1.095-3) => 3000 x 0.762 = £2,286 · Difference of £1 due to rounding . Note that discounting at 9.5% gives a higher present value than discounting at 10% (£2,253)
Present Value of Annuity Cash Flows · An annuity is a finite series of identical annual cash flows · Simple annuities assume first cash flow is in one year Annuity Factors 5% 6% 7% 8% 9% 10% 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 1 0.952 0.943 0.935 0.926 0.917 0.909 0.901 0.ff93 D.ffff5 0.ff77 0.ff70 0.ff62 0.ff55 0.ff47 0.ff40 0.ff33 2 1.ff59 1.ff33 1.ffOff 1.7ff3 1.759 1.736 1.713 1.690 1.66ff 1.647 1.626 1.605 1.5ff5 1.566 1.547 1.52ff 3 2.723 2.673 2.624 2.577 2.531 2.487 2.444 2.402 2.361 .322 2.2ff3 2.246 2.210 .174 2.140 4.106 4 3.546 3.465 B.3ff7 3.312 3.240 3.170 B.102 3.037 2.974 2.914 2.ff55 2.79ff 2.743 5 4.329 4.212 4.100 B.993 B.ff90 3.791 B.696 3.605 B.517 .433 .352 3.274 2.690 .199 127 2.639 2.5ff9 .05ff .991 • Calculate the present value of £1,000 received annually for 3 years (first receipt in 1 year) if the discount rate is10%: • Present value = £1,000 x 2.4ff7 = £2,487 · Using a scientific calculator · Simple annuity formula: PV= FV (1 - 1+r) *) r TimeE Years ) Present Value= Future Cash Flow(1- ((1+Discount Rate) Discount Rate
· Simple annuity - first cash flow in one year · PV = cash flow x annuity factor (AF) for t years · i.e. PV = 1000 x 2.4ff7 (AF 3 years at 10%) = 2487 · Advance annuity - first cash flow today- Paid one year in advance so Today, 1 year, 2 year. · PV = cash flow x (1 + AF for t-1 years) · i.e. PV = 1000 x (1 + 1.736 (AF 2 years at 10%) = 2736 · Deferred annuity - first cash flow in two or more years PV = cash flow x AF for t years x discount factor (DF) for t-1 year(s) deferred · i.e. if first cash flow in 2 years, PV = 1000 x 2.4ff7 (AF 3 years at 10%) x 0.909 (DF 1 year at 10%) = 2261 Present Value