Question

In: Finance

You can invest in a​ risk-free technology that requires an upfront payment of $1.13 million and...

You can invest in a​ risk-free technology that requires an upfront payment of $1.13

million and will provide a perpetual annual cash flow of $115,000.

Suppose all interest rates will be either 9.7% or 4.7% in one year and remain there forever. The​ risk-neutral probability that interest rates will drop to 4.7% is 93%. The​ one-year risk-free interest rate is 8.1%​,

and​ today's rate on a​ risk-free perpetual bond is 5.5%. The rate on an equivalent perpetual bond that is repayable at any time​ (the callable annuity​rate) is 8.6%.

What is the NPV of investing​ today?

What is the NPV of waiting and investing​ tomorrow? The NPV if the rate goes up is $? The NPV if the rate goes down is $? The PV is?

Verify that the hurdle rate rule of thumb gives the correct time to invest in this case. The hurdle rule is $?

The NPV is >0 so should you invest now or wait?

Solutions

Expert Solution

What is the NPV of investing​ today?

Here the appropriate cost of capital to be used for capitalization of perpetual cash flows is todays's rate on a risk free perpetual bond = 5.5 %

NPV = Annual CIF / r - Upfornt Investment = 115,000 / (0.055) - 1130,000 = 960,909

What is the NPV of waiting and investing​ tomorrow?

Here we have to use discount rate in computing the present value = The​ one-year risk-free interest rate i= 8.1%​, For capitalizing the cash flows, we have use the rates as they were after one year ( i.e either 9.7 % or 4.7% )

The NPV if the rate goes up is $?

NPV rate go up = 115,000 / (0.097) - 1130,000 = 55567

The NPV if the rate goes down is $? The PV is?

NPV rate goes down = 115,000 / (0.047) - 1130,000 = 1316809

PV = Present value = [ 55567 * (0.07) + 1316809 * (0.93) ] / (1.081)

= [ 3889.69 + 1224632 ] / (1.081) = 1,136,467.80

Verify that the hurdle rate rule of thumb gives the correct time to invest in this case.

Here we have apply r = callable bond annuity rate = 8.6% for computing the NPV

NPV = 115000 / 0.086 - 1130,000 = 207,209.30

The hurdle rule is $? ..........   = 207,209.30 The NPV > 0 so should Invest now

Explanation. Hurdle rate method shall provide only an approximation. As seen in the above calulations the present value to invest after one year is 1,136,467.80 as against investing now of 960,909. Thus we should wait and invest after one year, but hurdle rate suggest immediate investment.


Related Solutions

Aasir can invest his money in risk-free asset and/or in a fund F. The risk-free asset...
Aasir can invest his money in risk-free asset and/or in a fund F. The risk-free asset provides a guaranteed return of 4%. The fund F provides expected return of 12% with volatility of 25%. If Aasir wants to limit his risk to no more than 20%, what is the highest expected return he can earn? If Aasir wants an expected return of at least 16%, what is the minimum possible volatility of his portfolio?
An investor can borrow or invest at a risk-free rate of 4%. The investor is a...
An investor can borrow or invest at a risk-free rate of 4%. The investor is a mean-variance utility maximize with a risk aversion coefficient A = 4. What is the expected return on an optimal allocation between the risk-free security and a risky portfolio with an expected return of 10% and a volatility of 20%?
Digital Organics (DO) has the opportunity to invest $1.13 million now (t = 0) and expects...
Digital Organics (DO) has the opportunity to invest $1.13 million now (t = 0) and expects after-tax returns of $710,000 in t = 1 and $810,000 in t = 2. The project will last for two years only. The appropriate cost of capital is 13% with all-equity financing, the borrowing rate is 9%, and DO will borrow $290,000 against the project. This debt must be repaid in two equal installments of $145,000 each. Assume debt tax shields have a net...
You have $91471 to invest in two stocks and the risk-free security. Stock A has an...
You have $91471 to invest in two stocks and the risk-free security. Stock A has an expected return of 10.99 percent and Stock B has an expected return of 11.09 percent. You want to own $29063 of Stock B. The risk-free rate is 3.76 percent and the expected return on the market is 12.08 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the...
You have $96433 to invest in two stocks and the risk-free security. Stock A has an...
You have $96433 to invest in two stocks and the risk-free security. Stock A has an expected return of 12.84 percent and Stock B has an expected return of 10.23 percent. You want to own $30572 of Stock B. The risk-free rate is 4.69 percent and the expected return on the market is 12.04 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the...
You have $76250 to invest in two stocks and the risk-free security. Stock A has an...
You have $76250 to invest in two stocks and the risk-free security. Stock A has an expected return of 10.7 percent and Stock B has an expected return of 11.1 percent. You want to own $30664 of Stock B. The risk-free rate is 3.78 percent and the expected return on the market is 12.87 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the...
You have $93395 to invest in two stocks and the risk-free security. Stock A has an...
You have $93395 to invest in two stocks and the risk-free security. Stock A has an expected return of 11.39 percent and Stock B has an expected return of 9.25 percent. You want to own $34661 of Stock B. The risk-free rate is 4.2 percent and the expected return on the market is 12.78 percent. If you want the portfolio to have an expected return equal to that of the market, how much should you invest (in $) in the...
You want to buy a car valued at $48,000. You will make an upfront down-payment of...
You want to buy a car valued at $48,000. You will make an upfront down-payment of $5,000 on the car, and borrow the rest of the money from your bank. Your bank will give you a 5-year loan at 2.5% APR compounded semi-annually. You plan to make biweekly payments (i.e., one payment every two weeks) on the loan. The bank requires that you make the first payment two weeks after you signed the loan contract. Find the answer to the...
You invest all your money into a risky asset and a risk-free asset. The risky asset...
You invest all your money into a risky asset and a risk-free asset. The risky asset has an expected return of 0.065 and a standard deviation of 0.25, the risk-free asset returns 0.025. What is the return on your combined portfolio if you invest 0.4 in the risky asset, and the remainder in the risk-free asset? Round your answer to the fourth decimal point.
Your division is considering 2 investment projects, each which requires an upfront expenditure of $25 million....
Your division is considering 2 investment projects, each which requires an upfront expenditure of $25 million. You estimate the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dollars). Year Project A Project B 0 -$25 -$25 1 $5 $20 2 $10 $10 3 $15 $8 4 $20 $6 a) What is the regular payback period for each of these projects? b) What is the discounted payback period for each...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT