Time Value of Money in Finance

How to price bonds, loans and shares as the present value of their cash flows, how to read implied returns and growth rates back out of market prices, and how cash flow additivity and no arbitrage set forward interest rates, forward exchange rates and option values.

1. 1. Present value and discount (zero-coupon) bondsA cash flow received later is worth less today, and a zero-coupon bond's price is simply its principal discounted back at the market rate.Video · 6 minFree13 min
2. 2. Coupon bonds and perpetual bondsA coupon bond is a bundle of zero-coupon cash flows, so its price is every coupon and the principal discounted at one rate: the YTM.13 min
3. 3. Level-payment instruments: mortgages and amortizing loansA fully amortizing loan is repaid with equal payments whose PV equals the amount borrowed; each payment is part interest, part principal.Video · 7 min12 min
4. 4. Valuing shares with dividend discount modelsA share is worth the present value of all the dividends it is expected to pay, and the growth pattern you assume decides which formula to use.14 min
5. 5. Implied returns on bondsWhen a bond's price is known, solve the valuation equation for the rate: that implied return is the market's expected return, provided its assumptions hold.13 min
6. 6. Required return, implied growth and the P/E ratioA share price embeds a joint view on return and growth: in the Gordon model, r = dividend yield + g, so knowing one lets you back out the other.14 min
7. 7. Cash flow additivity, no arbitrage and forward ratesValues of cash flows at the same date can be added and subtracted, so economically equivalent strategies must cost the same; implied forward rates are the rates that make this true.14 min
8. 8. No-arbitrage pricing of FX forwards and optionsThe same no-arbitrage logic sets forward exchange rates (two riskless deposits must end equal) and option values (a riskless share-plus-option portfolio must earn the risk-free rate).15 min