Sofia is a successful chef in San Francisco. She bought her restaurant 5 years ago for $10

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Question:

Sofia is a successful chef in San Francisco. She bought her restaurant 5 years ago for $10 million. Sofia payed down 20% and financed the remainder of the investment with a 20-year fixed-rate mortgage loan with 7% APR, monthly compounding and monthly payments. As a result of shelterin-place orders Sofia experienced a decrease in sales, but wants to keep the restaurant for delivery. After talking with other small business owners about cash management she is considering alternative options: As a result of the reduction of overall rates in the economy, Sofia was able to find an offer from an online bank for a 6% APR on a 15-year fixed-rate mortgage with monthly compounding and monthly payments. The Bank has a $50,000 fee for the appraisal of the place. One of Sofia friend mentioned about a government program helping Small Businesses. Due to administrative burden, Sofia can access the government program only with her current lender. The government program offers a refinancing option with a payment holiday for one year (i.e., no mortgage payment and no accrue interest, the balance remain the same as the one when the option is chosen). After one year the government program has a 7.5% APR 15-year fixed-rate mortgage with monthly compounding and monthly payments. Assume throughout the exercise that Sofia can invest at an APR of 7% with monthly compounding (hint: use this as her "cost of capital").

(a) What is Sofia's current mortgage payment? How much does she still owe on her current mortgage?

(b) What would be the new monthly payments after refinancing with the online bank? What would be the new monthly payments after taking the government program?

(c) Which of the three options (continue with the existing mortgage, refinance with the online bank, take the government program with the current bank) is better today from a financial perspective? How much cheaper would it be in present value terms than the second best option?

(d) Would Sofia's answer change if she needs cash today to continue operating the restaurant? (no additional calculations needed)