A credit card offers an interest rate of 18% pa, compounding monthly.

Find the effective monthly rate, effective annual rate and the effective daily rate. Assume that there are 365 days in a year.

All answers are given in the same order:

### r_\text{eff monthly} , r_\text{eff yearly} , r_\text{eff daily} ###

A firm changes its capital structure by issuing a large amount of equity and using the funds to repay debt. Its assets are unchanged. Ignore interest tax shields.

According to the Capital Asset Pricing Model (CAPM), which statement is correct?

A wholesale shop offers credit to its customers. The customers are given 21 days to pay for their goods. But if they pay straight away (now) they get a 1% discount.

What is the effective interest rate given to customers who pay in 21 days? All rates given below are effective annual rates. Assume 365 days in a year.

You're considering making an investment in a particular company. They have preference shares, ordinary shares, senior debt and junior debt.

Which is the safest investment? Which will give the highest returns?

Your friend just bought a house for $**1,000,000**. He financed it using a $**900,000** mortgage loan and a deposit of $**100,000**.

In the context of residential housing and mortgages, the 'equity' or 'net wealth' tied up in a house is the value of the house less the value of the mortgage loan. Assuming that your friend's only asset is his house, his net wealth is $100,000.

If house prices suddenly fall by **15%**, what would be your friend's percentage change in net wealth?

Assume that:

- No income (rent) was received from the house during the short time over which house prices fell.
- Your friend will not declare bankruptcy, he will always pay off his debts.

Your poor friend asks to borrow some money from you. He would like $1,000 now (t=0) and every year for the next 5 years, so there will be 6 payments of $**1,000** from t=0 to t=5 inclusive. In return he will pay you $**10,000** in seven years from now (t=7).

What is the net present value (NPV) of lending to your friend?

Assume that your friend will definitely pay you back so the loan is risk-free, and that the yield on risk-free government debt is **10**% pa, given as an effective annual rate.

Over the next year, the management of an **unlevered** company plans to:

- Make $
**5**m in sales, $**1.9m**in net income and $**2**m in equity free cash flow (EFCF). - Pay dividends of $
**1**m. - Complete a $
**1.3**m share buy-back.

Assume that:

- All amounts are received and paid at the end of the year so you can ignore the time value of money.
- The firm has sufficient retained profits to legally pay the dividend and complete the buy back.
- The firm plans to run a very tight ship, with no excess cash above operating requirements currently or over the next year.

How much new equity financing will the company need? In other words, what is the value of new shares that will need to be issued?

**Question 415** income and capital returns, real estate, no explanation

You just bought a residential apartment as an investment property for $**500,000**.

You intend to rent it out to tenants. They are ready to move in, they would just like to know how much the monthly rental payments will be, then they will sign a twelve-month lease.

You require a total return of **8**% pa and a rental yield of **5**% pa.

What would the monthly paid-in-advance rental payments have to be this year to receive that 5% annual rental yield?

Also, if monthly rental payments can be increased each year when a new lease agreement is signed, by how much must you increase rents per year to realise the 8% pa total return on the property?

Ignore all taxes and the costs of renting such as maintenance costs, real estate agent fees, utilities and so on. Assume that there will be no periods of vacancy and that tenants will promptly pay the rental prices you charge.

Note that the first rental payment will be received at t=0. The first lease agreement specifies the first 12 equal payments from t=0 to 11. The next lease agreement can have a rental increase, so the next twelve equal payments from t=12 to 23 can be higher than previously, and so on forever.

**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.

**Question 794** option, Black-Scholes-Merton option pricing, option delta, no explanation

Which of the following quantities from the Black-Scholes-Merton option pricing formula gives the **Delta** of a European **call** option?

Where:

###d_1=\dfrac{\ln[S_0/K]+(r+\sigma^2/2).T)}{\sigma.\sqrt{T}}### ###d_2=d_1-\sigma.\sqrt{T}=\dfrac{\ln[S_0/K]+(r-\sigma^2/2).T)}{\sigma.\sqrt{T}}###