1) A year ago, a friend of yours made a loan to a reliable local business you have both known for many years. The business is doing well, and looks very likely to pay back the loan. Your friend now needs to raise some cash urgently for other business investments, and wishes to sell her loan on to someone. Interest rates are 5% and she lent them $2,000 for 2 years at 5% exactly a year ago. The borrower paid last year's interest ($100) this morning, but is not due to pay anything more until a year from today, when they will pay $100 interest & $2,000 capital. What is the most money your friend could get for her loan note?
2) Now suppose that your friend had lent the money several years ago, when interest rates were higher, she lent them $2,000 at 10%. But interest rates are now 5%. One year from now your friend will receive $200 interest & $2,000 of capital. What is the most her loan is worth today?
3) Interest rates are 5% a year, and one share in a gas company called warmth pays a dividend of $2 today. The market believes that warmth will grow profits & dividends by 3% a year from next year forever. What is a share worth today?
i) The value of a loan at any time is calculated as the present value of the all future cash associated with the loan, this includes interest payments as well as the capital repayment. For calculating present value the relevant discounting rate is the current interest rate. In your friend's loan there are following ...
This solution provides calculations and explanations for questions regarding loans and shares.