ALM Lecture 2 Yas Suttakulpiboon ALM The Basics

ALM: Lecture 2 Yas Suttakulpiboon

ALM The Basics of ALM Today’s Class Financial statement analysis Intro to Derivatives Derivative Pricing Advanced Topics and RM Applications Forward Binomial Option Pricing Model Volatility Time value of money Futures Black-Scholes Formula Interest Rate and Bond Derivatives Bond Swap Hedging Value at Risk Duration and Convexity Matching Option Credit Risk

Time Value of Money and Interest Rate Yas Suttakulpiboon

Reading Berk and De. Marzo Chapter 4 -5

Agenda: Time Value of Money • The timeline • Three rules of time travel • Valuing a stream of cash flows • Calculating the NPV • Perpetuities and Annuities • The internal rate of return (IRR)

The timeline

Three rules of time travel • Combine the same cash flow at the same time • Moving cash flow forward • Moving cash flow backwards

Valuing a stream of cash flows

Problem • You have just graduated and need money to buy a new car. Your rich Uncle Henry will lend you the money so long as you agree to pay him back within four years, and you offer to pay him the rate of interest that he would otherwise get by putting his money in a savings account. • Based on your earnings and living expenses, you think you will be able to pay him $5000 in one year, and then $8000 each year for the next three years. If Uncle Henry would otherwise earn 6% per year on his savings, how much can you borrow from him?

Calculating the NPV • NPV = PV(benefits) - PV(costs) = PV(benefits - costs) • Problem • You have been offered the following investment opportunity: If you invest $1000 today, you will receive $500 at the end of each of the next three years. If you could otherwise earn 10% per year on your money, should you undertake the investment opportunity?

Perpetuities A perpetuity is a stream of equal cash flows that occur at regular intervals and last forever.

Annuities • An annuity is a stream of N equal cash flows paid at regular intervals. The difference between an annuity and a perpetuity is that an annuity ends after some fixed number of payments. Most car loans, mortgages, and some bonds are annuities. We represent the cash flows of an annuity on a timeline as follows.

Problems: Perpetuities or Annuities • You want to endow an annual MBA graduation party at your alma mater. You want the event to be a memorable one, so you budget $30, 000 per year forever for the party. If the university earns 8% per year on its investments, and if the first party is in one year’s time, how much will you need to donate to endow the party? • You are the lucky winner of the $30 million state lottery. You can take your prize money either as (a) 30 payments of $1 million per year (starting today), or (b) $15 million paid today. If the interest rate is 8%, which option should you take? • Ellen is 35 years old, and she has decided it is time to plan seriously for her retirement. At the end of each year until she is 65, she will save $10, 000 in a retirement account. If the account earns 10% per year, how much will Ellen have saved at age 65?

The Internal Rate of Return • Internal rate of return (IRR), defined as the interest rate that sets the net present value of the cash flows equal to zero.

Problem • Jessica has just graduated with her MBA. Rather than take the job she was offered at a prestigious investment bank—Baker, Bellingham, and Botts—she has decided to go into business for herself. • She believes that her business will require an initial investment of $1 million. After that, it will generate a cash flow of $100, 000 at the end of one year, and this amount will grow by 4% per year thereafter. What is the IRR of this investment opportunity?

Problem • Baker, Bellingham, and Botts, was so impressed with Jessica that it has decided to fund her business. In return for providing the initial capital of $1 million, Jessica has agreed to pay them $125, 000 at the end of each year for the next 30 years. What is the internal rate of return on Baker, Bellingham, and Botts’s investment in Jessica’s company, assuming she fulfills her commitment?

Homework 2 (Part 1) • Do problem sets on pages 166 -171 (Berk and De. Marzo) • Each one of you have to complete 10 questions: question number 5, 10, 15, 20, …, 50 • Submit your work here before next class: https: //drive. google. com/open? id=1 ZZq. PEMh. Asck. XO 31 mtu. Up. ARAEJj 58 Vs 6 K

Agenda: Interest Rates • Interest rate quotes and adjustments • The determinants of interest rates • Risk and taxes • The opportunity cost of capital

What is interest rate?

The determinants of interest rates • Demand for Money and Supply of Money • Fed Fund Rate • Nominal vs Real Interest Rates • Real = Nominal + Inflation

Yield Curve • The relationship between the investment term and the interest rate is called the term structure of interest rates. We can plot this relationship on a graph called the yield curve.

NPV in real life… use yield curve

Yield curve is random!

Why different companies can borrow at different interest rates?

Risk and interest rates Suppose the U. S. government owes your firm $1000, to be paid in five years. Based on the interest rates in Figure 5. 4, what is the present value of this cash flow? Suppose instead Gap Inc. owes your firm $1000. Estimate the present value in this case.

After-tax interest rates • If the cash flows from an investment are taxed, the investor’s actual cash flow will be reduced by the amount of the tax payments. After-tax interest rate = r(1 -t)

The opportunity cost of capital • opportunity cost of capital (or more simply, the cost of capital), which is the best available expected return offered in the market on an investment of comparable risk and term to the cash flow being discounted. • The cost of capital is clearly relevant for a firm seeking to raise capital from outside investors. In order to attract funds, the firm must offer an expected return comparable to what investors could earn elsewhere with the same risk and horizon

Homework 2 (Part 2) • Each one of you picks one academic paper discussing a relationship between interest rates and insurance companies/insurance industry • Make a brief summary using Power. Point Presentation. You need to include the following: • • Title, Author, Year, Journal Research question and why does it matter? Literature review Methodology Data Main results Conclusion • Next class: 5 -10 minute presentation of each paper • Submit your Power. Point Presentation before next class here: https: //drive. google. com/open? id=1 ZZq. PEMh. Asck. XO 31 mtu. Up. ARAEJj 58 Vs 6 K • Check this out: https: //riskx. teachable. com/courses/186049/lectures/3197355

ALM The Basics of ALM Today’s Class Financial statement analysis Intro to Derivatives Derivative Pricing Advanced Topics and RM Applications Forward Binomial Option Pricing Model Volatility Time value of money Futures Black-Scholes Formula Interest Rate and Bond Derivatives Bond Swap Hedging Value at Risk Duration and Convexity Matching Option Credit Risk