Question 31 DDM, perpetuity with growth, effective rate conversion
What is the NPV of the following series of cash flows when the discount rate is 5% given as an effective annual rate?
The first payment of $10 is in 4 years, followed by payments every 6 months forever after that which shrink by 2% every 6 months. That is, the growth rate every 6 months is actually negative 2%, given as an effective 6 month rate. So the payment at ## t=4.5 ## years will be ## 10(1-0.02)^1=9.80 ##, and so on.
A stock pays semi-annual dividends. It just paid a dividend of $10. The growth rate in the dividend is 1% every 6 months, given as an effective 6 month rate. You estimate that the stock's required return is 21% pa, as an effective annual rate.
Using the dividend discount model, what will be the share price?
Which firms tend to have low forward-looking price-earnings (PE) ratios?
Only consider firms with positive earnings, disregard firms with negative earnings and therefore negative PE ratios.
Question 434 Merton model of corporate debt, real option, option
A risky firm will last for one period only (t=0 to 1), then it will be liquidated. So it's assets will be sold and the debt holders and equity holders will be paid out in that order. The firm has the following quantities:
##V## = Market value of assets.
##E## = Market value of (levered) equity.
##D## = Market value of zero coupon bonds.
##F_1## = Total face value of zero coupon bonds which is promised to be paid in one year.
What is the payoff to debt holders at maturity, assuming that they keep their debt until maturity?
Calculate the price of a newly issued ten year bond with a face value of $100, a yield of 8% pa and a fixed coupon rate of 6% pa, paid semi-annually. So there are two coupons per year, paid in arrears every six months.
An investor owns a whole level of an old office building which is currently worth $1 million. There are three mutually exclusive projects that can be started by the investor. The office building level can be:
- Rented out to a tenant for one year at $0.1m paid immediately, and then sold for $0.99m in one year.
- Refurbished into more modern commercial office rooms at a cost of $1m now, and then sold for $2.4m when the refurbishment is finished in one year.
- Converted into residential apartments at a cost of $2m now, and then sold for $3.4m when the conversion is finished in one year.
All of the development projects have the same risk so the required return of each is 10% pa. The table below shows the estimated cash flows and internal rates of returns (IRR's).
| Mutually Exclusive Projects | |||
| Project | Cash flow now ($) |
Cash flow in one year ($) |
IRR (% pa) |
| Rent then sell as is | -900,000 | 990,000 | 10 |
| Refurbishment into modern offices | -2,000,000 | 2,400,000 | 20 |
| Conversion into residential apartments | -3,000,000 | 3,400,000 | 13.33 |
Which project should the investor accept?
Question 785 fixed for floating interest rate swap, non-intermediated swap
The below table summarises the borrowing costs confronting two companies A and B.
| Bond Market Yields | ||||
| Fixed Yield to Maturity (%pa) | Floating Yield (%pa) | |||
| Firm A | 3 | L - 0.4 | ||
| Firm B | 5 | L + 1 | ||
Firm A wishes to borrow at a floating rate and Firm B wishes to borrow at a fixed rate. Design a non-intermediated swap that benefits firm A only. What will be the swap rate?
Question 825 future, hedging, tailing the hedge, speculation, no explanation
An equity index fund manager controls a USD500 million diversified equity portfolio with a beta of 0.9. The equity manager expects a significant rally in equity prices next year. The market does not think that this will happen. If the fund manager wishes to increase his portfolio beta to 1.5, how many S&P500 futures should he buy?
The US market equity index is the S&P500. One year CME futures on the S&P500 currently trade at 2,155 points and the spot price is 2,180 points. Each point is worth $250.
The number of one year S&P500 futures contracts that the fund manager should buy is: