Title LM02 The Time Value of Money in Finance IFT Notes.pdf ✅

LM02 The Time Value of Money in Finance 2025 Level I Notes © IFT. All rights reserved 1 LM02 The Time Value of Money in Finance 1. Introduction...........................................................................................................................................................2 2. Time Value of Money in Fixed Income and Equity .................................................................................2 3. Implied Return and Growth..........................................................................................................................10 4. Cash Flow Additivity .......................................................................................................................................13 Summary...................................................................................................................................................................21 Required disclaimer: IFT is a CFA Institute Prep Provider. Only CFA Institute Prep Providers are permitted to make use of CFA Institute copyrighted materials which are the building blocks of the exam. We are also required to create / use updated materials every year and this is validated by CFA Institute. Our products and services substantially cover the relevant curriculum and exam and this is validated by CFA Institute. In our advertising, any statement about the numbers of questions in our products and services relates to unique, original, proprietary questions. CFA Institute Prep Providers are forbidden from including CFA Institute official mock exam questions or any questions other than the end of reading questions within their products and services. CFA Institute does not endorse, promote, review or warrant the accuracy or quality of the product and services offered by IFT. CFA Institute®, CFA® and “Chartered Financial Analyst®” are trademarks owned by CFA Institute. © Copyright CFA Institute Version 1.0
LM02 The Time Value of Money in Finance 2025 Level I Notes © IFT. All rights reserved 2 1. Introduction In this learning module we will apply time value of money principles to value financial assets. This learning module covers: • Calculating the present value of fixed-income and equity instruments based on their expected cash flows. • Calculating implied bond and stock returns given their current market prices. • Applying the cash flow additivity and no-arbitrage principles to calculate implied forward interest rates, forward exchange rates, and option values. 2. Time Value of Money in Fixed Income and Equity The relationship between present value (PV) and future value (FV) of a cash flow is: FVt = PV(1 + r)t where: r = stated discount rate per period t = number of compounding periods With continuous compounding the relationship can be expressed as: FVt = PVert We can also rearrange the above equations and express present value in terms of future values as: PV = FVt (1 + r) t PV = FVt e rt Fixed-Income Instruments and the Time Value of Money Fixed-income instruments are debt instruments such as a bond or a loan. Depending on the types of cash flows provided we can divide them into three types: • Discount instruments • Coupon instruments • Annuity instruments Discount instruments: A debt security that does not pay interest but is instead issued at a deep discount. At maturity the security is redeemed for its full face value. The difference between the face value and issue price represents interest earned over the life of the instrument. E.g., zero-coupon bonds.

LM02 The Time Value of Money in Finance 2025 Level I Notes © IFT. All rights reserved 4 The present value of a coupon paying bond can be calculated as: PV of bond = PMT (1+r)1 + PMT (1+r)2 + ⋯ + PMT+FV (1+r)N where: PMT = coupon payment per period FV= par value of the bond paid at maturity r = market discount rate N = number of periods until maturity Example The coupon rate on a bond is 4% and the payment is made once a year. The time to maturity is five years and the market discount rate is 6%. What is the bond price per 100 of par value? Solution: Start by drawing a timeline for the cash flows. The par value of the bond or principal is $100. A coupon payment of $4 is made every year. At maturity (at the end of five years), a payment of $104 (principal of $100 + coupon of $4) is made. We are required to calculate the present value of bond at time t = 0. For that, we discount all the future cash flows at the market discount rate of 6%.