Opportunity to Make an Investment

¶ … opportunity to make an investment of $900,000. If you make this investment now, you will receive $120,000, $250,000 and $800,000 one, two, and three years from today, respectively. The appropriate discount rate for this investment is 12.00%.

Should you make the investment?

What is the net present value (NPV) of this opportunity?

If the discount rate is 11.00%, should you invest? Compute the NPV to support your answer.

In order to find out it it's reasonable to make an investment we need to compare present value (PV) and cost of investment, if PV is smaller than cost of investment then we should not make an investment.

Present value can be calculated using the following formula:

PV = $120,000 / (1+.12) + $250,000 / (1+.12)2 + $800,000 / (1+.12)3 = $875,865.53.

As we can see present value is $875,865.53, which is smaller than cost of investment ($900,000) so we should not make an investment.

Net Present Value can be calculated using the following formula:

where the time of the cash flow the total time of the project the discount rate

Ct - the net cash flow (the amount of cash) at time t.

C0 - the capital outlay at the beginning of the investment time (t = 0) (from (http://en.wikipedia.org/wiki/Net_present_value)

or NPV= PV - C0

NPV= $875,865.53 - $900,00

NPV=-$24,134.47

Net Present value of this opportunity is -$24,134.47 which means that this investment project should be rejected.

c. NPV = -$900,000 + $120,000 / (1+.11) + $250,000 / (1+.11)2 + $800,000 / (1+.11)3 =

Because NPV is negative (-$4,033.18) this investment project should be rejected.

2. Consider two bonds, a and B. The coupon rates are 10.00% and the face values are $1,000.00 for both bonds. Both bonds have annual coupons. Bond a has 20 years to maturity while bond B. has only 10 years to maturity.

a. What are the prices of the two bonds if the relevant market interest rate for both bonds is 10.00%?

b. If the market interest rate increases to 12.00%, what will be the prices of the two bonds?

c. If the market interest rate decreases to 8.00%, what will be the prices of the two bonds?

Solution:

a. In order to calculate bond prices we first need to evaluate values: Present Value Interest Factor (PVIF), Present Value Interest Factor for an Annuity (PVIFA) which will give price of bond using the following formula:

Price of bond= PVIF * Redemption value + PVIFA * interest payment per period. Present Value Interest Factor and Present Value Interest Factor for an Annuity are defined by the following formulas:

PVIF = 1/(1+i) n

Present Value Interest Factor

PVIFA (i, n) = (1-1/(1+i) n) / i

Present Value Interest Factor for an Annuity

FOR BOND a:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 10%

10% $1,000 Annual 20-20-10.00% annual 10.00% 20-10.00%

Annual interest payments for this bond will be $100 and redemption value is 1000.

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 20 periods and n=10%

PVIF= 1/(1+0.1)^20

PVIF=0.1486436

PVIFA= (1- 1/(1+.1)^20)/.1

PVIFA=8.513564

Now we can evaluate price of bond:

Price of bond= PVIF * Redemption value + PVIFA * interest payment per period. Present Value

Price of bond= 0.1486436*1000 +8.513564*100= $148.64+$851.356

Price of bond= $1,000

So, price of bond a is $1,000

FOR BOND B:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 10%

10% $1,000 Annual 10-10-10.00% annual 10.00% 10-10.00%

Annual interest payments for this bond will be $100 and redemption value is 1000

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 10 periods and n=10%

PVIF= 1/(1+0.1)^10

PVIF=0.385543

PVIFA= (1- 1/(1+.1)^10)/.1

PVIFA=6.144567

Now we can evaluate price of bond:

Price of bond= PVIF * Redemption value + PVIFA * interest payment per period. Present Value

Price of bond= 0.385543*1000 +6.144567*100= $385.54.64+$614.45

Price of bond= $1,000

So, price of bond B. is $1,000 b. For market interest rate equal to 12%:

Price for bond a:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 12%

10% $1,000 Annual 20-20-12.00% annual 12.00% 20-12.00%

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 20 periods and n=12%

PVIF= 1/(1+0.12)^20

PVIF=0. 103667

PVIFA= (1- 1/(1+.12)^20)/.12

PVIFA=7.469444

Price of bond= 0.103667*1000+7.469444*100=$851

Price of bond a = $851

Price of bond B:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 12%

10% $1,000 Annual 10-10-12.00% annual 12.00% 10-12.00%

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 10 periods and n=12%

PVIF= 1/(1+0.12)^10

PVIF=0.321973

PVIFA= (1- 1/(1+.12)^10)/.12

PVIFA=5.650223

Price of bond= 0.321973*1000+5.650223*100=$886.99

Price of bond B = $886.99 for market interest rate equal to 8%:

Price for bond a:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 8%

10% $1,000 Annual 20-20 8.00% annual 8.00% 20 8.00%

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 20 periods and n=8%

PVIF= 1/(1+0.08)^20

PVIF=0. 214548

PVIFA= (1- 1/(1+.08)^20)/.08

PVIFA=9.818147

Price of bond= 0. 214548*1000+9.818147*100=$1,196.36

Price of bond a = $1,196.36

Price for bond B:

Market interest rate is equal Coupon rate is equal Face value Frequency Number of years to maturity Number of Periods Discount rate annually Discount rate per period n, periods r, per period 8%

10% $1,000 Annual 10-10 8.00% annual 8.00% 10 8.00%

Now we need to calculate PVIF and PVIFA.

For calculation of PVIFA (i, n) and PVIF I is equal to 10 periods and n=12%

PVIF= 1/(1+0.08)^10

PVIF=0.463193

PVIFA= (1- 1/(1+.08)^10)/.08

PVIFA=6.710081

Price of bond= 0.463193*1000+6.710081*100=$1,134.19

Price of bond B = $1,134.19

3. Scubaland, Inc. is experiencing a period of rapid growth. Earnings and dividends per share are expected to grow at a rate of 18.00% during the next two years, 15.00% in the third year, and 6.00% thereafter. Yesterday, Scubaland paid a dividend of $1.15. If the required rate of return on the stock is 12.00%, what is the price of a share of the stock today?

As it's stated in the problem that Scubaland paid dividend of $1.15 yesterday, then we can assume that this amount is dividend for the last year. Using growth rates provided in the problem we can calculate the value of dividends which are expected to be received in future:

Year growth Dividend

1.357 = 1.15*(1+0.18)

Dividend in year 4 will be equal to $1.95

No we can calculate present value of dividends starting from the year 4.

PV (n-1)= D (n)/(r-g), where n- year #; r- rate of return on the stock; g- growth rate of the stock:

D3= 1.95/(12%-6%)=32.5