A stock is expected to pay a dividend of $15 in one year (t=1), then $25 for 9 years after that (payments at t=2 ,3,...10), and on the 11th year (t=11) the dividend will be 2% less than at t=10, and will continue to shrink at the same rate every year after that forever. The required return of the stock is 10%. All rates are effective annual rates.

What is the price of the stock now?

**Question 337** capital structure, interest tax shield, leverage, real and nominal returns and cash flows, multi stage growth model

A fast-growing firm is suitable for valuation using a multi-stage growth model.

It's **nominal** unlevered cash flow from assets (##CFFA_U##) at the end of this year (**t=1**) is expected to be $**1** million. After that it is expected to grow at a rate of:

**12**% pa for the next two years (from t=1 to 3),**5**% over the fourth year (from t=3 to 4), and**-1**% forever after that (from t=4 onwards). Note that this is a negative one percent growth rate.

Assume that:

- The nominal WACC
**after**tax is**9.5**% pa and is not expected to change. - The nominal WACC
**before**tax is**10**% pa and is not expected to change. - The firm has a target debt-to-
**equity**ratio that it plans to maintain. - The inflation rate is
**3**% pa. - All rates are given as
**nominal**effective annual rates.

What is the levered value of this fast growing firm's assets?

**Question 498** NPV, Annuity, perpetuity with growth, multi stage growth model

A business project is expected to cost $100 now (t=0), then pay $10 at the end of the third (t=3), fourth, fifth and sixth years, and then grow by 5% pa every year forever. So the cash flow will be $10.5 at the end of the seventh year (t=7), then $11.025 at the end of the eighth year (t=8) and so on perpetually. The total required return is 10℅ pa.

Which of the following formulas will **NOT** give the correct net present value of the project?

A stock is expected to pay its first dividend of $**20** in **3** years (t=3), which it will continue to pay for the next nine years, so there will be **ten** $20 payments altogether with the last payment in year 12 (t=12).

From the thirteenth year onward, the dividend is expected to be **4**% more than the previous year, forever. So the dividend in the thirteenth year (t=13) will be $20.80, then $21.632 in year 14, and so on forever. The required return of the stock is **10**% pa. All rates are effective annual rates. Calculate the current (t=0) stock price.

**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?