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?

**Question 1069** Multiples valuation, venture capital, elasticity, DuPont formula, multi stage growth model

Read the below excerpt of AFR journalist Vesna Poljak's article 'What’s a start-up really worth' from 24 November 2020:

If Charlie

Mungeris right that earnings before interest, tax, depreciation and amortisation are “bullshit earnings”, and presenting adjusted EBITDA is “basic intellectual dishonesty”, someone should ask the 96-year-old Berkshire Hathaway vice-chairman what he thinks ofrevenue multiples.It’s a necessary evil of this bull market that so many companies are now valued on multiples of their sales, as opposed to profits, typically because they don’t have any of the latter. It’s also impossible to ignore that real money investors are backing businesses at “multi-unicorn” valuations, meaning that capital is being allocated on an assumption lying somewhere between a considered ability to correctly recognise future growth, and magical thinking.

The idea is that, eventually, these businesses will arrive at a point where their constant reinvestment in sales and marketing, customer acquisition, and systems and process (all items that appear below the revenue line) will no longer be necessary, thereby allowing profits to suddenly crystallise.

Our baby unicorn is now a cloud-based workhorse with stunning margins, low operational costs, a market-dominant position and loyal customers totally

insensitive to price increases.Forecasts and evangelical founders are the natural enemies of a sound mind. “These businesses are very different compared to the typical mature business,” says PwC partner Richard

Stewart. “They’re very heavily intangible-asset focused so traditional accounting doesn’t describe the performance of the business well.“They’re also very risk intensive: it’s a bit like they’re climbing Everest, they’ve got halfway and there’s still a long way to the summit. The start-up sees how far they’ve come from base camp, the investor sees how far they have to go.”

EY partner Michael

Fenechsaid that once upon a time,revenue multipleswere used to value companies in very limited circumstances. “Now, revenue multiples have emerged as one of the primary valuation methodologies that people are using, which concerns people like myself.”A robust valuation should be underpinned, wherever possible, by cash-flow forecasts, Fenech says. “So if we see companies relying on

revenue multiples, our level of scepticism is often heightened and we start asking other questions.”

Which of the below statements is **NOT** correct?

You're considering starting a software company with an initial (t=**0**) cost of $**71**.

The first positive cash flow will be **$10** in one year (t=1), and will grow by **2**% pa for **3** years. So the next cash flows will be: **$10** at t=**1**;

**$10.2** (=10*(1+0.02)^1) at t=**2**;

**$10.404** (=10*(1+0.02)^2) at t=**3**;

**$10.6121** (=10*(1+0.02)^3) at t=**4**.

From t=**4** onwards, these positive cash flows will grow at the lower rate **-3**% pa (note the negative sign) in perpetuity. So the subsequent cash flows will be: **$10.2937** (=10*(1+0.02)^3*(1-0.03)^1) at t=**5**;

**$9.9849** (=10*(1+0.02)^3*(1-0.03)^2) at t=**6**;

**$9.6854** (=10*(1+0.02)^3*(1-0.03)^3) at t=**7**, and so on forever.

The required return is **10**% pa. What is the net present value (NPV) of starting this company? All results above are rounded to 4 decimal points, and answer options below to 2 decimal points. The NPV of starting this company is: