The owners of Annie's Homemade Ice Cream are deciding between buying land and building a $1,800$ square$-$feet ice cream shop or signing a five$-$year lease for $1,500$ square feet of retail space. If the company decides to buy land and build an ice cream shop, the total cost of the land, building, and paved parking lot is $$1,200,000.$ At the end of five years, the company estimates the market value of this commercial property would be $$1,300,000.$ If the company chooses to sign a lease, it would cost $$350,000$ to transform the unfinished leased space into an ice cream shop.

For simplicity, Annie's is assuming the following items would be the same across the five$-$year time horizon under the buy$-$and$-$build and lease alternatives:

Annual sales

Ingredients costs

Labor costs

Equipment costs

Working capital invested and released

All other operating costs besides those mentioned below

If the company chooses the lease option, it would pay annual rent of $$36,000.$ If Annie's chooses to buy$-$and build, some of its operating costs would be higher than the lease option. For example, under the buy$-$and$-$build option, Annie's would pay higher property taxes, insurance premiums, and utility expenses. The annual amount by which these operating costs exceed the lease option is $$15,000.$

$2.$ Assuming a disxount rate of $14\%$ and using a five year time horizon:

a$.$ What is the net present value of the relevant cash flows associated with the lease option?

b$.$ What is the net present value of the relevant cash flows associated with the buy and build option?

c$.$ Which of the two options is the least cost alternative?

d$.$ Given the assumed discount rate of $14\%$ what would have to be the market value of the commercial property at the end of five years to make Annie's indifferent when choosing between the leade and buy and build alternatives?

Assuming a discount rate of $14\%$ and using a five$-$year time horizon: