Question 58 NPV, inflation, real and nominal returns and cash flows, Annuity
A project to build a toll bridge will take two years to complete, costing three payments of $100 million at the start of each year for the next three years, that is at t=0, 1 and 2.
After completion, the toll bridge will yield a constant $50 million at the end of each year for the next 10 years. So the first payment will be at t=3 and the last at t=12. After the last payment at t=12, the bridge will be given to the government.
The required return of the project is 21% pa given as an effective annual nominal rate.
All cash flows are real and the expected inflation rate is 10% pa given as an effective annual rate. Ignore taxes.
The Net Present Value is:
In Australia in the 1980's, inflation was around 8% pa, and residential mortgage loan interest rates were around 14%.
In 2013, inflation was around 2.5% pa, and residential mortgage loan interest rates were around 4.5%.
If a person can afford constant mortgage loan payments of $2,000 per month, how much more can they borrow when interest rates are 4.5% pa compared with 14.0% pa?
Give your answer as a proportional increase over the amount you could borrow when interest rates were high ##(V_\text{high rates})##, so:
###\text{Proportional increase} = \dfrac{V_\text{low rates}-V_\text{high rates}}{V_\text{high rates}} ###
Assume that:
- Interest rates are expected to be constant over the life of the loan.
- Loans are interest-only and have a life of 30 years.
- Mortgage loan payments are made every month in arrears and all interest rates are given as annualised percentage rates (APR's) compounding per month.
A stock just paid a dividend of $1. Future annual dividends are expected to grow by 2% pa. The next dividend of $1.02 (=1*(1+0.02)^1) will be in one year, and the year after that the dividend will be $1.0404 (=1*(1+0.02)^2), and so on forever.
Its required total return is 10% pa. The total required return and growth rate of dividends are given as effective annual rates.
Calculate the current stock price.
Question 535 DDM, real and nominal returns and cash flows, stock pricing
You are an equities analyst trying to value the equity of the Australian telecoms company Telstra, with ticker TLS. In Australia, listed companies like Telstra tend to pay dividends every 6 months. The payment around August is called the final dividend and the payment around February is called the interim dividend. Both occur annually.
- Today is mid-March 2015.
- TLS's last interim dividend of $0.15 was one month ago in mid-February 2015.
- TLS's last final dividend of $0.15 was seven months ago in mid-August 2014.
Judging by TLS's dividend history and prospects, you estimate that the nominal dividend growth rate will be 1% pa. Assume that TLS's total nominal cost of equity is 6% pa. The dividends are nominal cash flows and the inflation rate is 2.5% pa. All rates are quoted as nominal effective annual rates. Assume that each month is exactly one twelfth (1/12) of a year, so you can ignore the number of days in each month.
Calculate the current TLS share price.
An American wishes to convert USD 1 million to Australian dollars (AUD). The exchange rate is 0.8 USD per AUD. How much is the USD 1 million worth in AUD?
An Indonesian lady wishes to convert 1 million Indonesian rupiah (IDR) to Australian dollars (AUD). Exchange rates are 13,125 IDR per USD and 0.79 USD per AUD. How many AUD is the IDR 1 million worth?
Question 574 inflation, real and nominal returns and cash flows, NPV
What is the present value of a nominal payment of $100 in 5 years? The real discount rate is 10% pa and the inflation rate is 3% pa.
Question 793 option, hedging, delta hedging, gamma hedging, gamma, Black-Scholes-Merton option pricing
A bank buys 1000 European put options on a $10 non-dividend paying stock at a strike of $12. The bank wishes to hedge this exposure. The bank can trade the underlying stocks and European call options with a strike price of 7 on the same stock with the same maturity. Details of the call and put options are given in the table below. Each call and put option is on a single stock.
| European Options on a Non-dividend Paying Stock | |||
| Description | Symbol | Put Values | Call Values |
| Spot price ($) | ##S_0## | 10 | 10 |
| Strike price ($) | ##K_T## | 12 | 7 |
| Risk free cont. comp. rate (pa) | ##r## | 0.05 | 0.05 |
| Standard deviation of the stock's cont. comp. returns (pa) | ##\sigma## | 0.4 | 0.4 |
| Option maturity (years) | ##T## | 1 | 1 |
| Option price ($) | ##p_0## or ##c_0## | 2.495350486 | 3.601466138 |
| ##N[d_1]## | ##\partial c/\partial S## | 0.888138405 | |
| ##N[d_2]## | ##N[d_2]## | 0.792946442 | |
| ##-N[-d_1]## | ##\partial p/\partial S## | -0.552034778 | |
| ##N[-d_2]## | ##N[-d_2]## | 0.207053558 | |
| Gamma | ##\Gamma = \partial^2 c/\partial S^2## or ##\partial^2 p/\partial S^2## | 0.098885989 | 0.047577422 |
| Theta | ##\Theta = \partial c/\partial T## or ##\partial p/\partial T## | 0.348152078 | 0.672379961 |
Which of the following statements is NOT correct?
Question 935 real estate, NPV, perpetuity with growth, multi stage growth model, DDM
You're thinking of buying an investment property that costs $1,000,000. The property's rent revenue over the next year is expected to be $50,000 pa and rent expenses are $20,000 pa, so net rent cash flow is $30,000. Assume that net rent is paid annually in arrears, so this next expected net rent cash flow of $30,000 is paid one year from now.
The year after, net rent is expected to fall by 2% pa. So net rent at year 2 is expected to be $29,400 (=30,000*(1-0.02)^1).
The year after that, net rent is expected to rise by 1% pa. So net rent at year 3 is expected to be $29,694 (=30,000*(1-0.02)^1*(1+0.01)^1).
From year 3 onwards, net rent is expected to rise at 2.5% pa forever. So net rent at year 4 is expected to be $30,436.35 (=30,000*(1-0.02)^1*(1+0.01)^1*(1+0.025)^1).
Assume that the total required return on your investment property is 6% pa. Ignore taxes. All returns are given as effective annual rates.
What is the net present value (NPV) of buying the investment property?