Corporate Finance Notes

You have just won the lottery. The prize is $10 million. When you go to claim your money, you learn that the $10 million will be paid in 10 equal installments of $1 million, and the first payment will be a year from now. Assume a discount rate of 10%. What is the value of the prize to you?

PV = C (1 - 1 ) r (1+r)^T PV = $1M/10% (1 - 1/(1+10%)^10) PV = 6.14M

Suppose your family house has a current value of $200,000. The government wants to buy it and pay for it with perpetual annual payments. It promises an initial payment of C next year and to increase this amount every year by 1%. Assume the discount rate is 8% annually. What should C be? (do not include decimal points)

PV = C / r - g 200,000 = C / 8% - 1% 7% x 200,000 = C C = $14,000

The government will pay you $12,000 annually. Assume a discount rate of 8%. Suppose the government promises to increase the payment by 1% every year. What is the present value of your house?

PV = C / r - g PV = 12,000 . .07 PV = $171,428.57

Maturity Date

final payment date of a bond

Securities

financial instruments that are readily tradable (publicly traded stocks and bonds)

Secondary Market

markets where investors trade securities with each other and the issuer isn't involved Lets say you purchase a note in the primary market that promises 10 semi-annual coupons plus the principal at maturity. You collect the first 8 coupons and at that point you decide to sell the note to a different investor. You transfer ownership of the note to this new investor at a price. The new investor will then only receive the remaining 2 coupons and principal payment, unless they choose to sell before maturity

Definition of stockholder

owners of stocks in a corporation who are entitled to all earnings of a company after all the obligations are paid

Stock

ownership interest in a company

Future Value

r = the rate of return over the period N = time The formula to derive the future value one period from now of a given amount of money today

Definition of a stock

represents ownership in a corporation

Bond

securities between 2 parties in which 1 party promises future payments to the other until a final payment date Securities that governments or corporations sell to raise money from investors When investors buy bonds, they are essentially lending money to the government or corproations that sold them the securities Investors receive not only the amount they lent, but also an interest on it

What are other words for stock

shares and residual income security

Issuing a Security

the act of selling a security for the first time Investors buy these newly-minted bonds at a price determined in the auction

Bond Certificate

the document describing the coupon rate, face value, and maturity date

Issuer

the entity that first issues a security

There are 3 strips: 1 has a price of 98.52 and a yield of 1.5% 2 has a price of 96.12 and a yield of 2% 3 has a price of 93 and a yield of 2.45% Suppose you want to value a coupon bond that pays $4 in year 1, $4 in year 2, and $104 in year 3

the way to do this is to discount each cash flow by the yield from the corresponding maturity PV = 4/(1+1.5%) + 4/(1+2%)^2 + 104/(1+2.45%)^3 = 104.51

Definition of Limited Liability

they can't lose more than their investment If you have stock in a company and at some point in the future the company doesn't have enough funds to pay all of its debts and goes bankrupt, the creditors can't go after your personal asset for the amount the company still owes them stockholders have limited liability

Why are treasuries safe

they promise to pay US dollars, and the Federal Reserve can always bring more dollars if necessary

How do you get the stock of firms who go several years without paying its first dividend (aka tech firms)?

we would need to replace the dividend for the first few yers with a 0 and have. positive value for the dividends only after some years

Primary Market

where investors buy newly-issued securities Investors buy these newly-minted bonds from the Treasury at a price determined in the auction Over time, if investors decide to keep the bond, the Treasury makes coupon and principal payments to them Investors who buy the bonds in the primary market don't have to keep them until maturity

Calculate the yield to maturity of a strip with maturity of 5 years that is currently trading at $94.38

yT = (100/94.38)^1/5 - 1 1.16%

Equation for computing the yield of a strip

yT = (100/P)^(1/T ) - 1

Strips

zero-coupon bonds (they pay no coupons and at maturity pay the face value) that are created by brokerage houses

You are a bond analyst working for a hedge fund. A bond you follow has face value 100, has a coupon rate of 5% (paid once a year) and matures in 5 years. You are trying to find if there is any profitable trading strategy. You've done extensive research and have formed your opinions on future economic conditions. As a result, you expect that there will soon be a major shift in the yield curve. The current and the expected yield curve is shown below: Year 1 Current 1% Expected 3% Year 2 Current 1.5% Expected 2.5% Year 3 Current 2% Expected 3.5% Year 4 Current 3% Expected 4% Year 5 Current 5% Expected 5% Calculate the price of the bond based on the expected yield curve $ ______(keep two decimal points)

$100.67

The yield of 1yr, 2yr, 3yr STRIP are 1%, 2%, 3%. Calculate the price of the coupon bond with face value of 100, coupon rate of 5%, annual payments, and maturity of 3 years.

5/1.01 + 5/1.02^2 + 105/1.03^3 = 105.85

Rate of Return

= Gain / Initial Investment The gain experienced over a period of time

Growing Perpetuity

A cash flow pattern in which cash flows grow at a constant rate and last forever PV = C / r - g

Perpetuity

A cash flow stream in which all the cash flows are the same and go on forever PV = C / r

The Yield Curve

A common way to represent the yields of different bonds is by a graph The yield curve represents the annual rate of return an investor can obtain at a specific point in time by investing in STRIPs of different maturities E.x. if you buy a strip with a 1 year maturity, you get a 0.61% annual return

The Payback Rule

Accept projects in which you will cover the initial investment in a short amount of time First compute the Payback Period - the number of years it takes to recoup your investment Second compare the payback period with a cutoff number If the payback period is lower than the cutoff, you accept the project

You have three projects under consideration. Project A requires an investment of $10M and has an NPV of $2M. Project B requires an investment of $5M and has an NPV of $2M. Project C requires an investment of $5M and has an NPV of $1.5M. Which project(s) should you take?

All of them as they are all positive NPV projects

How do you compute the value of any financial asset?

Compute the present value of the cash flows the asset generates using Opportunity Cost of Capital (the rate of return offered by alternative investments) as a discount rate

How do you compute the price of a stock?

P0 = DIV1/(1+rE) + DIV2/(1+rE)^2 + DIV3/(1+rE)^3 +...+ DIVT/(1=rE)^T + PT/(1+rE)^T The stock price is the present value of all future dividends PT = Price you get from the sale rE (discount rate) we use is the rate of return that can be earned on other investments that are as risky as the stock we are considering

You have three projects under consideration. Project A requires an investment of $10M and has an NPV of $2M. Project B requires an investment of $5M and has an NPV of $2M. Project C requires an investment of $5M and has an NPV of $1.5M. Which project(s) should you take if you have a budget to invest of only $10M?

PI = NPV / Initial Investment PI project B: 2/5 = 0.4 PI project C: 1.5/5 = 0.3 PI project A: 2/10 = 0.2 Should invest in B and C. That gets us to our max, $10M

If your investment pays back $110 1 year from now and $121 2 years from now, what is the present value of these cash flows? The cost of capital is 10%.

PV = $110/(1.1%) + $121/(1.1%^2) = $200

Suppose that a bank offers you a 5% annual rate of return. You want to have $126 at the end of the year. How much money do you need to deposit today?

PV = $126 / (1 + 0.05)^1 PV = $120

You are an investment manager at a buyout firm and are evaluating buying a large US-based toy company. The projected cash flows of the transaction are: Year 1 0.2, Year 2 0.3, Year 3 0.35. The opportunity cost of capital = 15% You estimate that you would be able to sell the firm at $1.8 billion (exit value). How much are you willing to pay for this firm.

PV = 0.2/(1+15%) + 0.3/(1+15%)^2 + 0.35+1.8/(1+15%)^3 PV = 0.174 + 0.227 + 1.41 PV = 1.81 The maximum you will be willing to pay for this firm is $1.81 billion OR can do the NPV function in excel

Your family owns a house that is acquired by the government. The government doesn't pay you any money up front, but agrees to pay you $12,000 every year starting next year in perpetuity. Assume a discount rate of 8%. What is the current value of this action to your family?

PV = 12,000 / 8% PV = $150,000

Your firm wants to borrow $1 million and repay this loan in 10 equal annual installments. The first installment will be one year from now. The bank charges an interest rate of 10%. What will your annual installment be? (Hint: the present value of your payments using a discount rate of 10% should equal the amount you borrow) Enter the answer with two decimal points.

PV = C (1 - 1 ) r (1+r)^T 1,000,000 = C/10% (1 - 1/(1+10%)^10) C = $162,745.39

You are a bond analyst working for a hedge fund. A bond you follow has face value 100, has a coupon rate of 5% (paid once a year) and matures in 5 years. You are trying to find if there is any profitable trading strategy. You've done extensive research and have formed your opinions on future economic conditions. As a result, you expect that there will soon be a major shift in the yield curve. The current and the expected yield curve is shown below: Year 1 Current 1% Expected 3% Year 2 Current 1.5% Expected 2.5% Year 3 Current 2% Expected 3.5% Year 4 Current 3% Expected 4% Year 5 Current 5% Expected 5% Calculate the price of the bond based on the current yield curve? (use 2 decimal digits)

$101.23

2 types of payments bonds make

1) Coupon - the promised interest payments of a bond that are paid throughout the life of the bonds 2) Principal/Face Value - the amount the bond pays back at each maturity date

Your biotech startup investment project is expected to earn a 10% return per year. Meanwhile, the rate of return of all your other investment projects with similar risk is 12%. What is the IRR of your biotech startup investment?

10%

Suppose your family house has a current value of $200,000. The government wants to buy it and pay you a constant amount every year forever starting next year. How much should this annual payment be? Assume a discount rate of 8%.

200,000 = x / 8% The annual payment should be $16,000

A group of bankers is evaluating buying a dying computer hardware company. The company is going to close down next year, but the bankers are wondering if they should buy it this year and, if so, how much they should buy it for. Computronics will make a one-time payment of $44,000 next year and then it will shut down. Suppose the bank is offering a 10% rate of return on deposits. How much should the bankers pay for Computronics?

Compute the value of computronics by calculating the present value of the cash flows it generates and use the rate of return offered by an alternative investment (the rate of return offered by the banks) as a discount rate PV = $44,000/(1 + 10%)^1 = $40,000 If the bankers deposit $40,000 in the bank today, they will have $44,000 next year

Suppose you purchase a bond with 1,000 dollars of face value with a coupon rate of 5% paid once per year. What is your cash flow at maturity date?

Coupon = Coupon Rate x Face Value / Number of Payments per year 5% x $1,000 / 1 = $50 At maturity, you will get the coupon payment of $50 + the principal back = $1,050

Coupon Equation

Coupon Rate x Face Value Number of payments per year

How to get the DIV1 variable in the Gordon Growth equation?

DIV1 = (1-b) x EPS1 1 - b is the inverse of the retention ratio (aka how much of the firm's earnings it pays out as dividends) EPS = earnings per share

Compute the amount of money you will have after 2 years if you deposit $100 dollars today. Assume that the rate of return per year is 10%.

FV = $100 x (1 + 0.1)^2 FV = $121

Firm A pays out 20% of its earnings as dividends and Firm B pays out 30% of its earnings as dividends. Both firms have the same return on investment. Which firm has higher growth rate?

Firm A - Firm A retains more for investment and therefore has a higher growth rate than Firm B

Suppose that today is August 15, 2020 and you are considering buying a US Treasury bond in the secondary market with a coupon rate of 3.7% and maturity date of August 15, 2023. Assume that the coupons are annual. Suppose that the price of the bond today is $107.94 (price it is trading at in the secondary market). Bond prices are expressed per $100 of face value. What are the payments you will receive?

First compute the cash flows associated with the purchase of a bond with $1,000 of face value 107.94 x 10 = 1079.4 This is just the price of 107.94 per $100 of face value times 10, as the bond we are purchasing has face value of 1,000 Next compute how much the annual coupons are Coupon = Coupon Rate x Face Value / Number of Payments per year 3.7% x $1,000 / 1 = $37 You will receive $37 on 8/15/21, $37 on 8/15/22, and $1,037 on 8/15/23

Difference between the IRR and the Cost of Capital (r)

IRR: - a measure of profitability, which is a function of a project's cash flows only - it is an intrinsic characteristic of the project Opportunity Cost of Capital - the rate of return that one could earn by investing in other projects with similar risk characteristics - can be higher, lower, or the same as the IRR, depending on the relative attractiveness of the project under consideration and other alternatives

Comparing IRR with NPV

If the NPV and IRR rule recommend the same action, go with the recommendation But, if the 2 rules disagree, you should follow the NPV rule because IRR is a profitability measure that is not informative about the scale of the project

Relationship between Yield and Bond Price

If the price of the bond decreases, the yield goes up If the price of the bond goes down, you need a higher yield to restore equality The bond's cash flows are fixed since they are determined by the bond certificate. Therefore, if you can buy the bond at the lower price but get the same cash flows, your return (yield) must be higher

Internal Rate of Return (IRR)

Internal Rate of Return = the specific discount rate (or rate of return) at which the NPV of a project is 0 IRR is a measure of the profitability of a project

Which of the following investments do you prefer? Investment A: generates $100 in 5 years. Investment B: generates $120 in 8 years. The opportunity cost of capital for both projects is 5%.

Investment A: PV = $100/(1 + 0.05)^5 = $78 Investment B: PV = $120/(1 + 0.05)^8 = $81 I prefer Investment B

Limitations of the Payback Rule

It disregards information beyond the cutoff period. If the cutoff was 2, we would rejected the project even though it had a large payoff of $400 in year 3. It simply adds the cash flows and doesn't take into account the time value of money

Consider a project with cashflows: Year 0 -1,000, Year 1 250, Year 2 250, Year 3 500, Year 4 100 What is the payback period? Should you accept this project?

It is 3 years. $250 + $250 + $300 = $1,000 (your initial investment) You should accept it if the cutoff is 4 years because the payback period is below the cutoff.

Now suppose that the project has no cash flows in years 1 to 5, has a cash flow of $44,000 in year 6 that then grows at a rate of 2% forever. The discount rate is 10%. How does this value of this project compare to the one above?

It is less than because the cash flows are identical, but they start later, so the PV is lower.

Jane is considering investing in a plant to manufacture handsets. The project requires an investment of $100 million today. In 1 year, this project will pay $25 million. In 2 years, it will pay $35 million. In 3 years, it will pay $45 million. In 4 years, it will pay $55 million. Assume the cost of capital for this project is 15%. Should she invest?

NPV = -100M + 25M/(1+15%) + 35M/(1+15%)^2 + 45M/(1+15%)^3 + 55M/(1+15%)^4 NPV = $9,238,817.76 Jane should take this project because the NPV is positive

Recall the Computronics example. The price of Computronics is $40,000 today and the firm pays a single cash flow next year of $44,000. What is the NPV of buying Computronics if the discount rate is 10%?

NPV = -40,000 + 44,000/(1+10%)^1 NPV = 0

You are considering making a sequel of a well known movie. There are 2 ways in which you can do this: you can invest $50 million today and receive $80 million in year 1 OR you can invest $120 million today and obtain $180 million in year 1. The cost of capital is 25%. Which way should you go with?

NPV of Option 1 $14,000,000 (NPV is positive, so the NPV rule says to invest) IRR of Option 1: 60% (60% IRR beats the cost of capital of 25%, so the IRR rule says to invest) NPV of Option 2: $24,000,000 (NPV is positive, so the NPV rule says to invest) IRR of Option 2: 50% (50% IRR beats the cost of capital of 25%, so the IRR rule says to invest) The 2 rules disagree. IRR says to go with Option 1 but NPV says to go with option 2. You should follow the recommendation of the NPV rule and choose Option 2 because NPV is expressing dollars today and takes into account the scale of the project

Suppose that a project has no cash flows in years 1-4 and has a cash flow of $44,000 in year 5 that then grows at a constant rate of 2% forever. The discount rate is 10%. What is the value of this project

Need to adjust the growing perpetuity formula to account for the cash flows starting in year 5 and not year 1 First find the present value of $44,000 at year 4 using the growing perpetuity formula PV4 = 44,000 / 10% - 2% = $550,000 Next find the present value of $550,000 at year 0 using the standard PV formula PV0 = $550,000 / (1+0.1^4) = $375,657.40

Will you be interested in buying Computronics at $42,000?

No because depositing the money in the bank yields a 10% return, which is higher than the 5% investment if we buy Computronics at $42,000.

Use the Gordon growth model formula to compute the price of a stock that will pay a $5 dividend per share next year and the dividend is expected to stay at $5 forever. Assume 5% cost of equity.

P0 = DIV1 / (rE - g) P0 = $5 / 5% = $100

What is the Gordon Growth Model

P0 = DIV1 / (rE - g) the equation for cases when a firm increases its dividend at a constant rate (g) aka the dividend stream is a growing perpetuity

Treasury Bills

bonds with a maturity of 1 year or less, zero coupon bonds

Treasury Bonds

bonds with maturities of 10-30 years, pay semiannual coupons

Let's compute the share price of 3 different firms: Firm A: - EPS of $10 - discount rate of 10% - retention ratio of 0 - Reinvestment Rate of Return of N/A Firm B: - EPS of $10 - discount rate of 10% - retention ratio of 40% - Reinvestment Rate of Return of 10% Firm C: - EPS of $10 - discount rate of 10% - retention ratio of 40% - Reinvestment Rate of Return of 15%

Price of Firm A: - rE is given: 10% - DIV1 (the dividend amount next period) will be $10 per share since firm A pays 0% of its earnings out as dividends - the dividend growth rate (g) is given by multiplying the retention ratio (b) and the reinvestment rate of return (RIR) --> 0 x N/A = 0 --> g = 0 - Plug into the Gordon Growth Equation P0 = $10 / (10% - 0%) = $100 Price of Firm B: - rE is 10% - DIV 1 (the dividend amount next period) will be $10 x (1-40%) --> $10 x 60% --> $6 - the dividend growth rate (g) is given by multiplying the retention ratio (b) and the reinvestment rate of return (RIR) --> 40% x 10% --> 16% - Plug into the Gordon Growth Equation P0 = $6 / (10% - 16%) = -$100 Price of Firm C: - rE is given: 10% - DIV1 (the dividend amount next period) will be $10 x (1-40%) --> $10 x 60% --> $6 - the dividend growth rate (g) is given by multiplying the retention ratio (b) and the reinvestment rate of return (RIR) --> 40% x 15% --> 6% - Plug into the Gordon Growth Equation P0 = $6 / (10% - 6%) = $150

Company is considering buying an investment product sold by Citigroup that requires a payment of $100,000 today and generates a payoff of $120,000 next year What is the rate of return?

Rate of Return = Gain / Initial Investment Gain = $120,000 - $100,000 = $20,000 So $20,000 / $100,000 = 20%

Capital Budgeting

Refers to the process corporations use to decide which projects to take The NPV and IRR rules are the most commonly used rules

What is your return if you buy Computronics at $42,000?

Return = $44,000 - $42,000 = $2,000 Rate of Return = $2,000/$42,000 = 4.76%

The return that Jane obtains by investing in the project (the IRR of the project) is 18.93%. The return she could obtain by investing in an alternative project with similar risk ® is 15%. Should Jane take the project?

Since the return on the project beats the return on alternative projects, Jane should invest in it.

Suppose you are considering a project that requires an investment of $100 right now. You believe that next period you will get $110 from this investment. This project has no other cash flows. Find the IRR

The IRR is the rate of return (r) at which the NPV of this project is 0 0 = -100 + 110/(1 + r) IRR = 10%

The new biotech project you want to invest in requires an initial investment of $200 million. It will pay off $240 million in 1 year. Compute the IRR of this investment project

The IRR is the rate of return (r) at which the NPV of this project is 0 0 = -200 + 240/(1 + r) r = 20%

Net Present Value aka the equation for the present value of multiple cash flow

The NPV formula also includes the cash flow in year 0 (the cash flow today), which is oftentimes the money you paid to buy the firm (negative) NPV = CF0 + CFT/(1+r)^T

Profitability Index

The NPV of a project Project's initial investment Shows you the bang for the buck A profitability index of 0.2 means that the project creates 0.2 dollars of value today for each dollar invested

What is a risk premium

The additional return offered by the asset to compensate the investor for bearing the risk

Annuity

The cash flows are constant, but it only lasts for a fixed number of periods PV = C/r {1 - 1/(1+r)^T}

Difference Between Coupon Rate and Yield

The coupon rate is written in the bond certificate and it is used to compute the coupon payments The yield is the rate of return an investor obtains by buying the bond and receiving all payments until maturity. The yield is a function of both the bond's cash flows and its current market price

In what cases is the growth rate variable in the Gordon Growth equation higher?

The growth rate is higher either when the firm retains more (higher b) or when it earns a higher return on investment (higher RIR)

How to get the g variable in the Gordon Growth equation?

The growth rate of earnings and dividends is: g = b x RIR b is the retention ratio - the % of the firms earnings that the firm retains for investment - 1-b is the % of the firms earnings that the firm pays out as dividends RIR is the Reinvestment Rate of Return - the rate of return equity holders get on new investments

What does the price of a bond depend on

The price of the bond will depend, among other things, on when you buy it → the price you pay for the bond at issuance vs 8 coupons in should factor the number of coupons you have left and the principal

Present Value aka Discounting

The process of computing the present value of a future cash flow

Discount Rate

The rate of return used for discounting

Yield to Maturity or the Yield

The yield is the rate of return you obtain by investing in a bond and holding it until maturity When investing in bonds, we call the IRR the yield to maturity or the yield

Treasury Notes

bonds with maturity of 2-10 years, pay semiannual coupons

How are shares sold and traded?

There are 2 ways you can buy stocks 1) You can buy socks from the firm itself. This happens when a firm wants to raise capital. In this case, the firm issues new shares and sells them to investors. Suppose a firm has a single owner (founder) and that she has 10 shares. The firm issues 5 new shares and sells them to an investor. The number of shares outstanding increase from 10 to 15 and the firm collects the amount paid by the investor. 2) You can buy stocks from other investors. Consider the firm just described with a single owner holding 10 shares. Imagine that this shareholder needs cash or wants to sell some of her shares for some reason. She sells 5 of her own shares to 1 investor. In this case, the number of shares outstanding doesn't change (10) and the amount paid for the shares ends up in the bank account of the original shareholder. This transaction doesn't involve the firm at all. This is majority of the trading activity that happens in the NYSE, Nasdaq, or any international stock exchanges.

You purchase a bond that requires an initial investment of $1,079.40 and, in return, we obtain cash flows of $37 (1 and 2 years from now) and $1,037 (3 years from now). What is this bond's yield?

Use Excel and calculate the IRR 1%

ConEd is in the energy sector. Imagine that it will pay a dividend of $2.8 per share next period and you expect this dividend to grow at 3%. Also, assume the cost of equity is 6.5%. What should be the price of ConEd today?

Use the Gordon Growth formula: P0 = DIV1 / (rE - g) P0 = $2.8 / (6.5% - 3%) = $80

Imagine ConEd just paid a dividend of $2.8 per share yesterday (instead of next period), and you expect this dividend to grow at 3%. Assume cost of equity is 6.5%. The price of ConEd today is $____

Use the Gordon Growth formula: P0 = DIV1 / (rE - g) The dividend of $2.8 has already been paid so if it's not part of the dividend stream an investor would get if she buys the stock today Instead, the first dividend this investor receives is the dividend next year of $2.8 x 1.03% = $2.88 And P = D1/(r-g) → $2.88/(6.5%-3%) = $82.4

The NPV Rule

Used for capital budgeting The NPV Rule says that whenever you are in a situation in which you have one project under consideration and the decision is whether to take or reject the project, you should take it every time the NPV is positive Also, if you are considering multiple projects but can only take some of them, you should go with, out of all possible combinations of projects, the combination with the highest NPV r = the expected rate of return that this firm could obtain by investing in a different project with similar risk

The IRR Rule

Used for capital budgeting Whenever you are in a situation in which you have one project under consideration and the decision is whether to take or reject the project, you should take the project every time the IRR is higher than the cost of capital (r) If you have to pick among many projects, you may think to pick the project with the highest IRR, but this can sometimes fail

What can we calculate using prices of government bonds?

We can use prices of government bonds to calculate the risk-free rate, which is critically important to valuation

Discounting The Yield Curve

We can use the prices of strips to compute the value of a coupon bond

How to discount risky cash flows (equation)

We can't use the yield of government bonds to discount the cash flows of risky projects projects because we use, as the opportunity cost of capital, the rate of return offered by assets with similar risk to the project we are valuing (and government bonds aren't risky) r = risk free rate + the risk premium

"Price of a bond"

When we talk about the price of a bond, we refer either to the price at which the bond is issued or its price in the secondary market

Profitability Index Rule

When you are facing a situation in which you have multiple projects and you must pick only a subset of them because you can't finance them all, pick the projects with the highest profitability index First compute the profitability index of each project Then sort projects from the one with the highest profitability to the one with the lowest profitability index Pick as many high PI projects as you can before reaching your budget

The initial investment required to start a project is $1million and its NPV is $0.9million. Should you invest in this project?

Yes. NPV rule says to invest when NPV is positive. Here, the initial investment amount is irrelevant since this information has been included in the NPV calculation.

Zero Coupon Bond

a special type of bond that pays no coupons, the only payment these bonds make is the face value at maturity