Question

The Vaughn Inc., a manufacturer of low-sugar, low-sodium, low-cholesterol TV dinners, would like to increase its market share in the Sunbelt. In order to do so, Vaughn has decided to locate a new factory in the Panama City area. Vaughn will either buy or lease a site depending upon which is more advantageous. The site location committee has narrowed down the available sites to the following three very similar buildings that will meet their needs.

Building A: Purchase for a cash price of $615,000, useful life 28 years.
Building B: Lease for 28 years with annual lease payments of $71,570 being made at the beginning of the year.
Building C: Purchase for $659,900 cash. This building is larger than needed; however, the excess space can be sublet for 28 years at a net annual rental of $6,870. Rental payments will be received at the end of each year. The Vaughn Inc. has no aversion to being a landlord.

Required:
In which building would you recommend that Brubaker Inc. locate, assuming a 12% cost of funds?

Answer 1

The new factory should be located in building C.

Step-by-step explanation:

This can be determined by comparing the present values of the cost of the three buildings and select the one with the lowest.

Building A: Purchase for a cash price of $615,000, useful life 28 years.

Present value of cost of building A = Cost of building A = $615,000

Building B: Lease for 28 years with annual lease payments of $71,570 being made at the beginning of the year.

Since the payments are to be made are the beginning of the year, the present value of the cost of the building can be calculated using the formula for calculating the present value (PV) of annuity due given as follows:

PV of B = P * ((1 - (1 / (1 + r))^n) / r) * (1 + r) .................................. (1)

Where ;

PV of B = Present value of the cost of building B = ?

P = Annual lease payments = $71,570

r = interest rate or cost of funds = 12%, or 0.12

n = number of years = 28

Substituting the values into equation (1) above, we have:

PV of B = $71,570 * ((1 - (1 / (1 + 0.12))^28) / 0.12) * (1 + 0.12)

PV of B = $640,018.55

Present value of the cost of building B = $640,018.55

Building C: Purchase for $659,900 cash. This building is larger than needed; however, the excess space can be sublet for 28 years at a net annual rental of $6,870. Rental payments will be received at the end of each year. The Vaughn Inc. has no aversion to being a landlord.

Cost of building C =$659,900

Since the annual rental from the sublet will be received at the end of each, the present value of the sublet can be calculated using the formula for calculating the present value of an ordinary annuity as follows:

PV of sublet = P * ((1 - (1 / (1 + r))^n) / r) …………………………………. (2)

Where;

PV of sublet = Present value of the annual rental from the sublet = ?

P = Annuity rental from the sublet = $6,870

r = interest rate or cost of funds = 12%, or 0.12

n = number of years = 28

Substituting the values into equation (2) above, we have:

PV of sublet = $6,870 * ((1 - (1 / (1 + 0.12))^28) / 0.12)

PV of sublet = $54,852.98

Present value of the cost of building C = Cost of building C - PV of sublet = $659,900 - $54,852.98 = $605,047.02

Conclusion

From the calculations above, we have the following:

Present value of cost of building A = $615,000

Present value of the cost of building B = $640,018.55

Present value of the cost of building C = $605,047.02

Since $605,047.02 which is the present value of the cost of building C is the lowest, the new factory should be located in building C.