# Time Value of Money / Capital Budgeting

1. You are the finance manager of this high-tech company and you have to prepare a final recommendation on the acquisition of some important equipment to be used in the manufacturing plant. There are two options, to buy it paying cash upfront or to lease it. The cost of the equipment if paid in cash upfront is $ 180,000 based on the quotes of several suppliers.

a) what option do you recommend if the lease option is based on 5 annual equal payments of $ 35,000 to be paid at the end of each year, plus a lump-sum payment of $ 30,000 at the end of the fifth year? The discount rate is 10%

b) all of a sudden, a supplier of the equipment calls you to tell you that if you buy it directly from them you could get a 15% discount. Does your recommendation change from a)?

2. You are the finance executive of a small business engaged in providing accounting services to other small businesses. You are interested in expanding your operations, but for that you need to improve your technology base. You're not sure if expanding is a good idea either. To increase your sales by $ 80,000 every year for the next five years based on your preliminary projections, you need better infrastructure. There are two alternatives: 1) you buy new IT equipment and software licenses with a lump-sum cost today for $ 70,000 plus annual cost of technical labor of $ 30,000 every year; or 2) you buy some IT equipment for a lump-sum of $ 40,000 today plus the annual cost of a contract with a supplier of software-as-a-service for $ 35,000. You know that the opportunity cost of the investment is 10% what would you recommend?

3. Ben and Jerry, two close friends of yours come to you somewhat agitated. They know you are a finance expert so they want you to help them sort out a situation. You ask them to sit down and explain the situation to you.

Your friends are successful entrepreneurs in the bakery business. They have been in the industry for several years now. The business is profitable, but strong competition limits their ability to keep growing. So they want to expand into a different business. They are considering the music industry, as they were before members of rock bands at college and have developed a few contacts in the local scene.

The problem is, they don't agree on how to value the prospects of their start-up. They both believe the capital structure of their new company would be the same as in the case of their bakery business, which is funded 50% with debt and 50% with common equity. Their disagreement stems from their understanding of what the required rate of return should be. Ben strongly believes that given their strong record in the bakery business they should require the same rate of return which is 9.5% (based on interest paid of 8% pre-tax rate to bank loans and 14.2% for the common equity component). Jerry strongly disagrees with that and believes that music is a more volatile business and therefore they should require another rate, maybe higher.

You, as the finance expert, recall that there is a very important finance principle that might be useful in supporting Jerry's arguments. You also happen to find in a finance magazine you have handy the following data:

Beta in the music industry: 2.25

Risk free rate: 4.5%

Risk premium: 7.5%

And the tax rate is the same, 40%. So you're ready to get things clarified here.

a) what finance principle is at work for your recommendation to your friends on how to proceed?

b) What should the required rate of return be for the music venture? Assume the new company will finance its operations 50% debt and 50% equity. (assume also that the new start-up can only get a bank loan at a higher interest rate of 9.5%)

c) Which rate should be used for project evaluation (capital budgeting) if the very first thing the friends want to do is to buy electronic equipment for their new music studio?

#### Solution Preview

1. You are the finance manager of this high-tech company and you have to prepare a final recommendation on the acquisition of some important equipment to be used in the manufacturing plant. There are two options, to buy it paying cash upfront or to lease it. The cost of the equipment if paid in cash upfront is $ 180,000 based on the quotes of several suppliers.

a) what option do you recommend if the lease option is based on 5 annual equal payments of $ 35,000 to be paid at the end of each year, plus a lump-sum payment of $ 30,000 at the end of the fifth year? The discount rate is 10%

In order to decide whether to buy or lease, we need to compare the present value of the two options. Under the buy option, the present value is $180,000.

Under the lease option we are to pay $35,000 at the end of each of the five years and $30,000 at the end of fifth year. The cash outflows are

Year 1 Year 2 Year 3 Year 4 Year 5

-35,000 -35,000 -35,000 -35,000 -65,000 ( -35,000+-30,000)

We need to find the present value of these. The discount rate is given as 10%. The present value can be found by discounting each of these payment by 10%. The sum of the PV is calculated as

-35,000/(1.1)+ - 35,000/(1.1)^2+ - 35,000/(1.1)^3+ - 35,000/(1.1)^4 + -65,000/(1.10^5

This gives us -31,818.20+-28,925.6+-26,296+-23,905.5+-40,359.9

The total value is -151,305.17

Since the outflow in lease is less than that of purchase, the lease option is better

b) all of a sudden, a supplier of the equipment calls you to tell you that if you buy it directly from them you could get a 15% discount. Does your recommendation change from a)?

If we get a 15% discount, the purchase price would be 180,000X85%=$153,000. This is still higher than the lease ...

#### Solution Summary

The solution has time value of money problems, lease and buy decision and capital budgeting