1. Questions-DCF and NPV

2. Q1)
First City Bank pays 7 percent simple interest on its savings account balances, whereas Second City Bank pays 7 percent interest compounded annually.
If you made a $62,000 deposit in each bank, how much more money would you earn from your Second City Bank account at the end of 9 years? 
The simple interest per year is: $62,000 × .07 = $4,340 
So, after 9 years, you will have: $4,340 × 9 = $39,060 in interest 
The account balance will be: Account balance = $62, ,060
Account balance = $101,060 
With compound interest, we use the future value formula: FV = PV(1 + r)t 
FV = $62,000(1.07)9FV = $113,984.47 The difference is: Difference = $113, – 101,060
Difference = $12,924.47

3. Q2)
Imprudential, Inc., has an unfunded pension liability of $570 million that must be paid in 20 years. To assess the value of the firm’s stock, financial analysts want to discount this liability back to the present.
If the relevant discount rate is 6.3 percent, what is the present value of this liability?
To find the PV of a lump sum, we use: 
PV = FV / (1 + r)tPV = $570,000,000 / PV = $167,961,430.66

4. Q3)
An investor purchasing a British consol is entitled to receive annual payments from the British government forever.
What is the price of a consol that pays $170 annually if the next payment occurs one year from today? The market interest rate is 4.8 percent.
A consol is a perpetuity. To find the PV of a perpetuity, we use the equation:  PV = C / rPV = $170 / .048PV = $3,541.67

5. Q4)
Wilkinson Co. has identified an investment project with the following cash flows:
If the discount rate is 8 percent, what is the present value of these cash flows?
3,406.47

6. Q5)
An investment offers $5,900 per year for 15 years, with the first payment occurring one year from now.
If the required return is 6 percent, what is the value of the investment today?
What would the value today be if the payments occurred for 40 years?
Same questions, but first payment occur 5 years from now
yrs: PVA = $5,900{[1 − (1 / )] / .06} = $57,302.27
yrs: PVA = $5,900{[1 − (1 / )] / .06} = $88,773.15

7. Q6)
Mark Weinstein has been working on an advanced technology in laser eye surgery. His technology will be available in the near term. He anticipates his first annual cash flow from the technology to be $181,000 received two years from today. Subsequent annual cash flows will grow at 4.1 percent in perpetuity
What is the present value of the technology if the discount rate is 10 percent?
PV = C / (r – g)PV = $181,000 / (.10 – .041)PV = $3,067,796.61 
It is important to recognize that when dealing with annuities or perpetuities, the present value equation calculates the present value one period before the first payment. In this case, since the first payment is in two years, we have calculated the present value one year from now. To find the value today, we simply discount this value as a lump sum. Doing so, we find the value of the cash flow stream today is:
PV = FV / (1 + r)tPV = $3,067, / ( )1PV = $2,788,906.01

8. Q7)
You need a 30-year, fixed-rate mortgage to buy a new home for $280,000. Your mortgage bank will lend you the money at an APR of percent for this 360-month loan. However, you can only afford monthly payments of $1,200, so you offer to pay off any remaining loan balance at the end of the loan in the form of a single balloon payment.
How large will this balloon payment have to be for you to keep your monthly payments at $1,200?
The amount of principal paid on the loan is the PV of the monthly payments you make. So, the present value of the $1,200 monthly payments is:
PVA = $1,200[(1 – {1 / [1 + (.0575 / 12)]360}) / (.0575 / 12)]PVA = $205,629.85  The monthly payments of $1,200 will amount to a principal payment of $205, The amount of principal you will still owe is:
 Principal remaining = $280,000 – 205,629.85Principal remaining = $74,370.15
This remaining principal amount will increase at the interest rate on the loan until the end of the loan period. So the balloon payment in 30 years, which is the FV of the remaining principal, will be:   
Balloon payment = $74,370.15[1 + (.0575 / 12)]360Balloon payment = $415,688.00