$($a$)$ Rivian has decided to invest in new automated driving tech and has announced a dividend cut. It set annual dividends for the coming years to $10,7,5$ and $3$ USD but also stated that dividends will grow at a rate of $3\%$ forever $($all amounts are per annum$).$ How much should the price be if the rate of return is $7\%?$

$($b$)$ Maersk is assessing two alternative shipment tagging systems for its system of warehouses.

The fully automated option will cost $330,000$ to install and will become obsolete after $6$ years. The semi$-$automated option is more expensive at $410,000$ but will remain operational for $11$ years. The benefits of both systems can be considered evenly spread during their lifetimes. Maersk intends to use own funds, currently deposited at $5\mathrm{.}5\%$ per annum. Which option is preferable?

$($c$)$ Consider a stock with a current price of $$45$ per share. The market capitalization rate on similar stocks is $11\%.$ The dividend one year from now is expected to be $$3$ and the dividend two years from now is expected to be $$4.$ After that the dividend is expected to grow at a constant rate. What is this constant dividend growth rate?