Question

Please i appreciate help to all parts of the questions,

Thanks.

2. The market value of Jane's honey fruit plant in year t is V(t) 10ev. (a) At what year is the honey fruit plant most valuable? Thus, based on (b) Assume that Jane's plant can be harvested only one time. If the real (c) If the real interest is 13%, when Jane should harvest the plant? Com- this answer, when do you suggest the plant to be harvested? interest is 10%, when Jane should harvest the plant? pare your results from previous two parts and comment on your find ings. Is this the result as you expected? Explain. (d) Assume the real interest rate is 10%. i. what will be the value of the honey fruit plant in 36 years (assum- ing the plan was not harvested before then)? ii. What will be the value of the honey fruit plant at the time of op- timal harvest? What is the value of her asset if she invests the proceedings from harvest into bank account that pays 10% annual rate for the rest of period until 36 years? iii. Compare previous two parts and advise Jane if it is indeed good to harvest plant at time you calculated in part (b). (e) Some honey fruit connoisseurs want to buy Jane's plant. What is the highest price she could charge for the plant now?

Answer 1

V(t) = 10 e^squareroot t, a) Present value of asset when i rate r , is compounded continuously, P = V(t) . e^-rt as dv(t)/dt rightdoublearrow 10 . e^squareroot t . 1/2 squareroot t = 5 e^squareroot t/ squareroot t > 0, as t uparrow, v(t), value of plant continuously uparrow, thus at t = infinity it is More valuable So plant should be harvested in Long Run b) Max P = v(t) . e^-rt = 10 . e^squareroot t . e^-rt = 10 e^squareroot t - rt So ln P = squareroot t - rt + ln 10 d ln P/dt rightdoublearrow 1/2 squareroot t - r = 0 So 1/2 squareroot t = r rightdoublearrow (1/2r)^2 = t So optional time to harvest rightarrow t = 1/4 r^2 So t = 1/4 (.10)^2 = 1 times 100/4 = 25 years Ans c) Now r = .13, t* = 1/4