Midterm

What is the YTM of a 2.5 year STRIP?

1.5% Since a STRIP is a zero-coupon bond, it has only one cash flow at maturity, so the YTM is simply the spot rate associated with that cash flow. In this case, the spot rate associated with a cash flow in 2.5 years is 1.5% from the term structure above.

If bonds are priced correctly, does a bond selling at a discount have a positive NPV? EXPLAIN.

No. If bonds are priced correctly, the price of the bond is equal to the present value of its cash flows. Thus, investing in the bond is a zero NPV project. That doesn't mean it's a bad investment. In calculating the PV of the bond's cash flows, you impose a certain required rate of return for investments like the bond. Buying the bond at the PV of these cash flows means that you are earning a fair return on your money—nothing great, nothing bad. A bond with coupons that are too small must sell at a discount in order to make buying it a fair deal (Zero NPV)—if it did not sell at a discount, it would be a negative NPV project!

Explain what a present value is in economic terms.

A present value tells you the amount you would need to have today to be just as happy as instead receiving the future value(s) at the future date(s). For example, if you are offered $100 per year for 10 years and your opportunity cost of capital is 10%, you would be indifferent between having $614.46 today or the $100 per year because you could invest the $614.46 today at 10% and create the $100 per year yourself.

Benchmark return

Discount rate that would be used to compute an investment's NPV

The goal of a financial manager is to maximize earnings.

FALSE. The goal of the financial manager is to increase the value of the company (increase shareholder wealth). Maximizing earnings is not the same thing. First of all, earnings are not cash flows, but are accounting constructs instead. You can't buy anything with earnings, buy you can buy things with cash flows. Second, which earnings should I maximize? I could maximize this year's earnings by not spending anything on future production, thus killing next year's earnings. How should I weight earnings in various years? Luckily NPV does all that for cash flows for us!

What is the IRR and what is the IRR decision rule?

The IRR is the discount rate that makes the NPV of the project equal to zero. Very loosely, you can think of it as the annualized rate of return you expect from taking the investment if the cash flows turn out as projected. Based on this latter intuition, the IRR decision rule tells you to accept a project if its IRR is greater than a predetermined hurdle or benchmark rate, which logically should be the project's opportunity cost of capital.

If you could only do one project, explain how would you rank the two projects?

I would rank them by NPV. NPV tells you how much value is created (or destroyed) by the projects. Your goal is to create the most value. IRR and Payback do not tell you value creation or destruction. IRR ranks on rate of return, which can translate into all kinds of value depending on the initial investment. Payback ranks on time until initial investment is paid back, which has nothing to do with value creation.

Why would your expected return on a bond be different from its yield‐to‐maturity?

If the bond has default (credit) risk, then your expected return will account for the fact that your expected cash flows are not the same as the promised cash flows. Since YTM is based on promised cash flows, it will be higher than your expected return in the presence of default risk.

You look in the paper and see that an 8% coupon bond with annual coupons, a par value of $1000, and 3 years to maturity is selling for $1053.46. Why is that price correct? It can only be correct if everyone agrees that they are just indifferent between buying the bond and re-creating the cash flows on their own. That is, if current market interest rates are 6% and the next coupon is due in one year, how could you use $1053.46 to exactly replicate the cash flows from the bond? Assume you have access to an investment instrument (like a bank account) that returns 6% per year. Explain how you would do this (you don't actually have to work through the numbers--just tell me in words how you would take $1053.46 and re-create the cash flows from the bond).

In class, we went through an example of how we would create an annuity using the PV of the annuity (see your notes in the annuity topic). This is the same thing. You would take the $1053.46 and invest it in your 6% investment instrument. After one-year, you would withdraw $80 to pay the first coupon, leaving the remaining balance to continue earning interest. You would do the same after 2 years. Finally, at the end of 3 years there should be exactly $1080 left in the account, which you would withdraw to pay the 6 coupon plus the principal of the bond.

Why the yield curve normally slopes upwards

Interest rates are expected to rise in the future due to economic conditions and supply and demand of credit. There is greater risk in entering into longer-term loans, so suppliers of credit require a premium in the form of higher rates for longer maturities. (a variant is that there is greater liquidity in short-term loans, so suppliers of credit require a premium to create long-term loans) There are more people willing to lend for shorter amounts of time and more companies/people looking to borrow for longer amounts of time, so the supply and demand imbalance leads to lower rates on short maturities and higher rates on long maturities.

Explain the NPV decision rule and the reasoning behind it.

The NPV decision rule says that you should accept a project if its NPV is positive and reject it if it is negative. This decision rule makes sense because the NPV measures the effect of the project on the value of the company, so if that effect is positive, you are increasing the value of the company and if it is negative, you would be decreasing the value of the company by accepting the project.

Explain the NPV decision rule.

The NPV decision rule says to value the benefits and costs of a decision in terms of their present values (cash value today) and then subtract the present value of the costs from the present value of the benefits to get the NPV. If the NPV is positive, then the decision creates value, adding value to the firm and the NPV decision rule says to take it and otherwise reject it.

What does the NPV calculation tell us? Why do we use it?

The NPV tells us whether the PV of the benefits outweigh the PV of the costs of undertaking a particular investment. In doing, so it gives us the dollar value of an investment's net effect on the value of the company. Since we want to maximize the value of the company (which maximizes the shareholders' wealth), we want to take projects that increase the value of the company. NPV tells us which ones do that.

What is the difference between a bond's expected return and its yield-to-maturity?

The YTM is the (average annualized) return you can expect to earn if you buy the bond at its current price, hold it to maturity and get all the cash flows as promised. Thus, the YTM is based on the promised cash flows for the bond. The expected return is based on the expected cash flows, which incorporate your assessment of the default (credit) risk of the bond—that is the chance that you will not get the cash flows as promised.

Yield to maturity

The annualized return you will get if you buy the bond at the stated price, hold it all the way to maturity, and get all of the promised cash flows on time. It is the rate which discounts all the future cash flows to equate it to the current market price of the bond.

The objective of a financial manager is to maximize the wealth of the shareholders (also known as maximizing the market value of the assets). Why is this a better objective than maximizing earnings? Why is it better than maximizing market share?

Maximizing earnings is an imprecise and misdirected goal. Earnings are the yearly accounting numbers created for tax purposes. They differ from cash flows due to things like depreciation expense. Shareholders care about cash flows, not earnings, so earnings are not the right numbers to maximize. Further, which earnings do we maximize? This year's next year's? The value of the assets will appropriately reflect all of the future cash flows generated by those assets.

What is the goal of the financial manager and why is it the right one?

The goal of the financial manager is to maximize the stock price (equity value of the firm). The stockholders are the owners of the firm and it is their money at risk. The value of the firm is the PV of the future cash flows it will generate. By choosing projects where the value today (PV) of all future benefits outweighs the value today (PV) of all future costs, the manager is creating value.

Explain the importance of the opportunity cost of capital.

The opportunity cost of capital drives our PV calculations because it is what our "r" should be (the discount rate) in our equations. The opportunity cost of capital identifies what return you are forgoing by making this investment (what is the next best opportunity with the same risk and timing). Thus, you discount the cash flows from a given investment using this opportunity cost. This determines whether the investment creates value relative to this next best alternative.

Would the YTM of a 1.5‐year 3% coupon Treasury bond be more than, less than, or equal to the YTM of a 1.5‐year 6% coupon Treasury bond? Explain.

More than—because the 3% coupon bond's coupon cash flows are smaller, the YTM calculation will put less weight on the lower rates, putting proportionately more weight on the par repayment (think of it like 15 vs. 1000 and 30 vs. 1000). Thus, while both YTMs will be close to and a bit less than 3%, the 3% coupon bond's YTM will be a little closer to 3% and thus more.

What determines the price of a bond and why?

The price of a bond is determined by the cash flows, the timing of those cash flows and the appropriate discount rates (as determined in the market). A bond is simply a package of cash flows, so its price is the present value of those cash flows.

Why does credit risk cause yield‐to‐maturity to increase?

The price of the bond will reflect the possibility of default, so as the credit risk increases (possibility of default increases), the price decreases. Since the YTM is based on the promised cash flows (like assuming no default), the lower price, compared to the promised cash flows will create a higher YTM.

If interest rates go down, will the principal repayment be a larger or smaller portion of the total value of the bond? Why?

The principal will become a larger proportion of the bond's value. While the bond's value will go up, the principal's value will go up more than proportionately because of the compounding effect of 200 periods of lower interest rates.

What are the two ways an asset can generate a rate of return?

The rate of return your earn from an asset comes from income generated from holding the asset (such as coupon payments on a bond) and capital gain (or loss) from selling the asset. If you sell the asset for more than you paid then part of your return comes from a capital gain. If you sell it for less than you paid, the part of your return comes from a capital loss.

What three components go into the required rate of return (interest rate)? Explain the components.

There is a real (risk-free) return: some compensation for parting with your money for some time even if you are sure to get it back. There is a component for inflation: some return to keep up with rising prices--to make me at least as well off at the end of the period (in terms of purchasing power) as I am today. Finally, there is a component for risk: some compensation for the chance that I might not get my money back.

Tell me what conditions would have to be satisfied in terms of the cashflows of the two projects.

There is no size disparity: both projects have the same initial investment There is no timing disparity: both projects have cash flows at the same intervals There is no "different lives" problem: both projects last for the same amount of time. Neither of the projects' cash flows changes signs more than once.

return

coupon + net gain,loss / price

Issues concerning payback

does not correspond to a measure of value on a firm, does not discount cash flows, ignores distant cash flows

What does the discount rate "r" represent? Explain why we use it to price money across time.

r represents our opportunity cost of money (what could we earn on our money in equivalent investments. Thus, if we want to price money across time, such as when we compare spending $100 today to get $110 tomorrow, we want to know what could we do with the $100 if we didn't take this investment. Using r to get the FV of the $100 if invested elsewhere tells us what our $100 would be worth in one year if invested elsewhere. Likewise, using r to discount the $110 back to today tells us how much money we would have to invest in our other opportunities earning r to have $110 in one year.

If the monthly payment is 111.02, Imagine you have the opportunity to repay the loan in annual (instead of monthly) installments over the same length of time. If the first payment is due 1 year after graduation, would the payment amount be more or less than $1332.24? What if the first payment were due on graduation day? WHY? Explain with words, not math.

$1332.24 is 12 times the monthly payment. We learned in class that if you wait one full year before making any payments, that annual payment will have to be more than just 12 times the monthly payments you would have made. The reason is that the bank is waiting to get its money and interest keeps accumulating on your principal. If you make monthly payments, you attack the principal immediately, reducing your total interest immediately.

If these are the cash flows, do you want the IRR to be more or less than the benchmark? +, ---- -, ++++

+, --- IRR < benchmark -, +++ IRR > benchmark IRR is the interest rate and you want it to be low when you are paying off a loan, but is high when you are receiving payments

Three reasons it might be inappropriate to use IRR

-First of all, the projects have different initial investments. Thus, it is inappropriate to use IRR, which is a rate of return, to compare them. The return doesn't tell me how much value I have added. I'd rather have 10% return on $1 million than 100% return on $1. -Second, the cash flows do not line-up. Rate of return comparisons only work for projects that have the same timing of cashflows. -Finally, project B has two "sign-switches." It's cash flows go from negative to positive and then negative again. This will produce multiple IRR's, leaving you unsure of what range of IRR's is the positive NPV range and which range is the negative range. In other words, you won't know if you're using the correct IRR. -Second, the projects have different lives. Rate of return comparisons do not make sense for projects of different lives since the rates of returns are computed over different periods.

The February 3rd WSJ contained this picture of the yield curve. It is inverted (yields for long-term bonds are lower than for short-term bonds). We talked about 3 factors that drive the yield curve and pointed-out that two of those factors tend to result in an upward-sloping (non-inverted) yield curve. The US Treasury announced on Feb 2nd that it was going to issue far fewer long-term bonds than in the past. Imagine your boss (either a bond trader or a chief financial officer trying to plan for a corporate debt issue) asks you what is going on. Identify which of the three factors driving the yield curve the Treasury's decision impacted and why it resulted in an inverted yield curve.

-Investors' expectations -Higher risk / lower liquidity for longer maturities -Higher demand for funds than supply of funds at long maturities all impact the shape of the yield curve. The first of these factors could make it slope up or down, depending on which way expectations go. However, #2 and #3 tend to add a premium onto longer-term rates, making the normal shape of the yield curve upward sloping. When the Treasury announced that it was going to issue fewer long-term bonds, it cut the demand for long-term funds considerably. Thus, if the demand for long term funds falls more in line with the supply of long-term funds, that supply/demand premium from point 3 goes away and the curve begins to invert.

The IRR and NPV criteria lead to the same investment decision when

1. The initial net cash flow is negative and all the subsequent cash flows are all positive (or positive followed by all negative cash flows) aka only one sign change 2. The investment decision does not affect the decision to accept or reject another investment as it does not rank projects correctly

What is a bond?

A long-term debt instrument in which a borrower agrees to make payments of principal and interest, on specific dates, to the holders of the bond.

What is the current yield of a one‐year, 3% coupon Treasury bond with a price of $1012? EXPLAIN whether the current yield is more than, less than, or equal to its YTM.

CY = 30/1012 = 0.0296 Because the coupon rate is greater than the relevant spot rates (2 and 2.5%), the bond is selling at a premium (1012). By buying the bond, you lock in a capital loss when it matures at 1000. Because the YTM includes both this effect and the effect of the income, it will be lower than the current yield, which only captures the effect of the income.

What is the current yield of a one‐year, 3% coupon Treasury bond with a price of $1012? EXPLAIN whether the current yield is more than, less than, or equal to its YTM.

CY = 30/1012 = 0.0296 Because the coupon rate is greater than the relevant spot rates (2 and 2.5%), the bond is selling at a premium (1012). By buying the bond, you lock in a capital loss when it matures at 1000. Because the YTM includes both this effect and the effect of the income, it will be lower than the current yield, which only captures the effect of the income.

What is the bond's current yield? If it is different from the bond's yield‐to‐maturity, explain the difference.

CY=30/1023.57 = 2.9% The current yield is different from the bond's yield‐to‐maturity because it only reflects the high rate of income that the bond will generate and does not account for the offsetting capital loss when the bond matures at $1000 even though you paid $1023.57 for it. The YTM accounts for all the cash flows over the whole life of the bond.

If the NPV of buying a bond is zero, does that mean it is a bad investment? EXPLAIN

No. It just means that you're earning a fair rate of return on your money. You pay the PV of the cash flows for the bond, which means that when you net-out your cost of the bond with the value of the bond, its NPV will be 0. However, when computing the PV of those cash flows, you used a discount rate which represented your required rate of return on investments like the bond. Thus, the NPV of 0 simply means that you are earning your required rate of return. It's not a bad investment, but it's not a great investment either. A full credit answer had to identify that the discount rate used to get the NPV is your required rate of return and that earning it means you're earning a fair return.

the remaining balance of a loan is always the

PV of the remaining payments

If current STRIP prices all drop, will the yield-to-maturity of coupon bonds increase or decrease? Explain.

STRIP prices are the prices of pure discount bonds. The only way STRIP prices would drop is if current market rates (spot rates) increase. The YTM of a bond is a weighted average of the spot rates associated with each of the cash flows in the bond. Thus, if the spot rates associated with the bond's cash flows increase, the YTM (as a weighted average of those rates) must also increase.

Explain why STRIP prices can be used to price U.S. government bonds.

STRIPS are created by "stripping" each of the individual cash flows from U.S. government bonds off and selling them individually. STRIP prices then tell us the value today of a $100 cash flow from the government on a particular date. Since two cash flows from the government on the same date can't have a different prices today (can't have different present values), we can use the price of a STRIP to figure-out the price per dollar for any amount of money to be received on that date. By doing this for each of the cash flow dates for the bond, we can price the bond.

Why is it a bad idea to use IRR to choose between projects?

Since IRR is only a rate of return, and does not measure actual value created or destroyed, it is a very poor tool for choosing between projects. One project may have a very high rate of return, but not create much value (like a 1000% return on a $100 investment) while another project may have a lower, but still acceptable, rate of return and create much more value (like a 15% return on $1M). If you can only undertake one project, you should choose the one that creates the most value. Also, the timing and relative size of the cash flows have to be exactly the same between the two projects in order for the IRR to always choose the right project.

Why does the yield curve normally slope upward?

The yield curve normally slopes up due to two factors which generally make rates for longer term loans greater than rates for shorter term loans. 1) The first is that people view longer‐term loans as riskier commitments because they are committing their money for a longer period of time, increasing the chance that they might need the money at some point when the market has moved against them. They must be compensated for this extra risk in the form of a higher return per year. 2) The second is that there are simply more entities looking to borrow at longer terms than there are looking to loan at those terms. The borrowers must offer a higher return per year in order to entice more lenders into the market to equate supply with demand.

Explain what a yield‐to‐maturity is

The yield to maturity is the annualized return you will get if you buy the bond at the stated price, hold it all the way until maturity and get all of the promised cash flows on time.

Name and explain one situation where it would be a mistake to rely on IRR.

There are lots of potential answers. One is that you should not rely on IRR to rank (choose among) projects. Since the IRR is a return, it won't identify a project's effect on value, so it won't help you identify which project generates the most value (it is influenced by the size of the initial investment). You also shouldn't rely on IRR when there is more than one sign change in the cash flow stream. In that case, there can be multiple IRRs and the IRR rule no longer applies. You would have to graph the NPV profile to know what to do.

Under what conditions would you not earn the yield-to-maturity of a bond you bought? Explain

There are many conditions that would cause this. The YTM will only correspond to your return if you hold the bond to maturity and receive all cash flows as promised, when promised. If there is any kind of default, you will not receive the YTM. Also, if you sell the bond before maturity, all bets are off. Depending on the direction that interest rates have moved, you could sell the bond at a loss or gain.

Assume that the term structure shows that the interest rate for 6-month maturities is 5.75% and the interest rate for 5 ½ year maturities is 6.25%. Interest rates increase by an increment of 0.05% for each 6-month interval in between, so that the average for the 11 rates is 6.00%. If you use 6% as your single discount rate to compute the PV of the package of cash flows from part a, will you underestimate, overestimate, or correctly value the bond? EXPLAIN.

We know that if we have to pick one rate when multiple rates are appropriate, the only single rate that will give us the correct value of the bond is the YTM. We also know that we can think about the YTM as a weighted average of the spot rates, where the weights are approximately proportional to the size of the cash flows to which they are attached. Given that, we know that the YTM for this bond will be above 6% because the largest cash flow occurs at the end, where the spot rate is 6.25%. Thus, if we use 6%, we will be using too low of a discount rate, which will result in too high of a present value (price) for the bond. So, the answer is that we will overestimate the price of the bond.

What's wrong with maximizing earnings per share?

Which earnings do you mean? I can maximize this year's earnings by not paying any expenses--of course we won't have a business next year. Do I maximize next year's earnings? Some weighted average? What are the weights? Are earnings even the actual amount of the money that shareholders get? No.

Explain what yield-to-maturity is

Yield to maturity is the discount rate that makes the present value of the bond's cash flows equal to the price of the bond. It represents all of the spot rates that go into pricing the bond. It is a complicated weighted average of the market spot rates.

What should be your discount rate in an NPV calculation and why?

You should use your opportunity cost of capital as your discount rate. The opportunity cost of capital identifies what return you are forgoing by making this investment (what is the next best opportunity with the same risk and timing). Thus, you discount the cash flows from a given investment using this opportunity cost. This determines whether the investment creates value relative to this next best alternative.

Why should you use the opportunity cost of capital as the discount rate?

Your discount rate should reflect the tradeoff between cashflows now and in the future. What drives that tradeoff is what you could do with cash flows today. When you make an investment, you are forgoing the next best opportunity for the use of your money (of equivalent risk and term). The return you could have earned in that other investment represents your opportunity cost of taking this investment instead. Thus the tradeoff between cash flows now and in the future is that forgone return—your opportunity cost of capital.

For any annuity, if the interest rate increases and the payment and timing of payments stays the same, (4 pts.) a. PV increases and FV increases b. PV decreases and FV increases <-- c. PV decreases and FV decreases d. PV increases and FV decreases

b. PV decreases and FV increases