Sugar Baby Corp. $($SBC$)$ is considering whether to build a refinery in the U$.$S$.$ state of Georgia to serve its North American market. SBC is based in the UK and processes raw sugar into premium gourmet sugar. Currently, SBC exports $100,000$kg of sugar per year to its North American customers and realizes a contribution margin of GBP $3$ per kg sold. SBC is certain that the new refinery in the U$.$S$.$ would meet all the current demand in North America and sales volume would likely increase. SBC does not foresee it will be able to sell any of the amount currently exported to North America once the new refinery is operational.

SBC estimates that it could sell $390,000$kg of sugar in North America during the first year ofoperations, and sales volume would grow at $5\%$ annually. SBC plans to price its product at USD $7\mathrm{.}70$ per kg$.$ Total operating costs are expected to be USD $3\mathrm{.}30$ per kg$.$ Both the sales price and operating costs are expected to keep pace with the U$.$S$.$ inflation rate forecast of $3\%$ per annum for the next $3$ years. The UK inflation rate is estimated at $4\mathrm{.}5\%$ per annum for the next $3$ years. The current USD$/$GBP spot rate is $1\mathrm{.}50.$ SBC believes that Relative PPP is the best predictor of future exchange rates.

The expected initial cost of the refinery is USD $4\mathrm{.}5$ million. SBC plans to finance this amount by a combination of debt and equity capital. The refinery will increase SBC$$s borrowing capacity by GBP $2$ million, and it plans to borrow only that amount. The State of Georgia will provide a concessionary loan of USD $1\mathrm{.}5$ million for a period of $3$ years at an interest rate of $7\mathrm{.}75\%.$ Principal on the loan will be repaid in equal installments over the life of the loan. At this point, SBC is uncertain whether to raise the remaining debt it requires through a domestic bond issue at $10\mathrm{.}75\%$ or a Eurodollar bond issue at $9\mathrm{.}5\%.$ SBC$$s all$-$equity cost of capital is $15\%.$

The U$.$S$.$ Internal Revenue Service will allow SBC to depreciate the new refinery over a $3-$year period on a straight$-$line basis. After that, the refinery equipment is expected to have substantial market value. The UK and the U$.$S$.$ have the same corporate tax rate of $35\%.$ There are no restricted funds available for SBC to offset the cost of the initial investment. SBC prefers to use Lessard$$s APV model for capital budgeting analysis.

a$)$ Compute the present value of after$-$tax incremental operating cash flows $($OCF$)$ in GBP$.$

b$)$ Compute the present value of the depreciation tax shields. Why are depreciation tax shields discounted at the domestic cost of debt?

c$)$ Compute the present value of the benefit from the concessionary loan in GBP$.$