# Calculating FV,Period,Rate,NPV and WACC

1.Present Value and Discounting

Discounting: How much is $1 that we receive in 2 years worth today (r=9%)?

2.How Long is the Wait?

If we deposit $5000 today into an account paying 10%, how long do we have to wait for it to grow to $10,000?

2.What Rate is Enough?

Assume the total cost of a college education will be $50,000 when your child enters college in 18 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your child's education?

4.NPV

You have an opportunity to invest in a business that will pay $200,000 in one year, $400,000 in two years, $600,000 in three years and $800,000 in four years. You can earn 12% per year compounded annually on a mutual fund that has similar risk. If it costs $1.2 million to start this business, what is the NPV & should you invest?

5.Break Even

Consider the following information for a big-screen television distributor:

Sales price per TV

$1,500

Variable costs per TV

$1,100

Fixed costs per year

$120,000

Depreciation per year

$20,000

Tax rate

35%

How many units must the distributor sell in a given year to break-even (in terms of accounting profit)?

6.Stock

A portfolio consists of 120 shares of Atlas stock, which sells for $50 per share, and 150 shares of Babcock

stock, which sells for $20 per share. What are the weights of the two stocks in the portfolio?

7.WAAC

Calculate the weighted average cost of capital for the Luxury Porcelain Company. The book value of Luxury's

outstanding debt is $50 million. Currently, the debt is trading at 120 percent of book value and is priced to

yield 12 percent. The 5 million outstanding shares of Luxury stock are trading at $20 per share. The

required return on Luxury stock is 18 percent. The tax rate is 25 percent.

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Solutions:

1. Discounting: How much is $1 that we receive in 2 years worth today (r=9%)?

Present Value = Future Value/(1+r)^n

Where r=rate of interest=9%

n= number of period=2 years

FV= Future Value = $1

Assume annual compounding

PV=1/(1+0.09)^2=$0.8417

2. How Long is the Wait?

If we deposit $5000 today into an account paying 10%, how long do we have to wait for it to grow to $10,000?

Future Value = Present Value*(1+r)^n

Where r=rate of interest=10%

n= number of period=? years

FV= Future Value = $10000

PV=$5000

Assume annual compounding

10000=5000*(1+0.1)^n

10000/5000=(1.1)^n

2=(1.1)^n

n=ln(2)/ln(1.1)= 7.27 years

3. What Rate is enough?

Assume the total cost of a college education will be $50,000 when your child enters college in 18 years. You have $5,000 to invest today. What rate of interest must you earn on your investment to cover the cost of your child's education?

Future Value = Present Value*(1+r)^n

Where r=rate of interest=?

...

#### Solution Summary

There are seven problems. Solution to first three problems explains the steps to determine FV, period and rate of interest for a given financial objective. Othert solutions describes the methodology to find out NPV and WAAC.